Download Decentralized Control Techniques Applied to Electric Power Distributed Generation in Microgrids

Decentralized Control Techniques
Applied to Electric Power Distributed
Generation in Microgrids
Juan Carlos Vásquez Quintero
Advisor
Dr. JOSEP MARIA GUERRERO ZAPATA
Programa de Doctorat en Automàtica, Robótica y Visió
Departament d’Enginyerı̀a de Sistemes,
Automàtica i Informàtica Industrial (ESAII)
A dissertation submitted for
the degree of European Doctor of Philosophy
June 10, 2009
ii
To my mom and the
memories of my father and grandmother.
iii
iv
ACKNOWLEDGEMENT
This work was supported by the Spanish Ministry of Science and Technology under
grants CICYT ENE 2006-15521-C03-01/CON and ENE2007-67878-C02-01/ALT.
First, I would like to thank deeply my father who was my role model, and to whom
I dedicate this thesis. I want to express sincere gratitude to all people who have helped
and inspired me and all my colleagues at Escola Industrial in Barcelona who made it a
comfortable place to work.
I would like to thank my advisor, Professor Josep M. Guerrero, for his guidance
and support throughout the course of this work. Equally, I am thankful to the SEPIC
research team for creating and maintaining an excellent academic environment, a factor
which had a positive impact on this work.
Also, I would like to thank Professor R. Teodorescu from IET department and his
team for allowing me to work at the Green Power Laboratory in Aalborg University, first
as student of the PERES course, second, because of his hospitality and support while I
was a guest and finally because thanks to that, several experimental results exposed in
this work based on line-interactive PV systems were obtained. Equally, thanks to the
Professor M. Liserre from the Department of Electrical and Electronic Engineering in
the Politecnico di Bari, Italy, where some experimental results based on novel power
quality conditioning functionalities were realized. Finally, I would also like to thank
Professor P. Rodriguez from UPC, for his scientific contributions and support.
v
vi
A BBREVIATIONS
f
Grid frequency [Hz]
T
Grid frequency period [s]
AND
S YMBOLS
Zg
Magnitude of the grid impedance [Ω]
Rg
Resistive part of the grid impedance [Ω]
Lg
Inductive part of the grid impedance [H]
Vg
Magnitude of the grid voltage [V]
Ig , Ic , IL
X
ipcc
Grid, converter and load current [A]
Inductor reactance [Ω]
PCC Measured current [A]
vpcc PCC Measured voltage [V]
−
→
I Current phasor at pcc [A]
−
→ →
−
Vg , Ig Grid Voltage and current phasors [V]
θg
Grid angle impedance [deg]
v
Measured grid voltage [V]
vref
Vc , Ic
θ′
Output voltage reference of the inverter [V]
Converter output voltage and current [V,I]
Measured grid angle [deg]
P, Q Active and reactive power injected into the grid [W,VAr]
Pmax
E
Maximum active power delivered by the VSI [W]
Voltage magnitude of the VSI [Vrms]
φ Phase of the VSI [deg]
Pc , Qc
Active and reactive power independent from the grid impedance [W,VAr]
P ∗, Q∗
Desired active and reactive power [W,VAr].
vii
Pi∗ , Q∗i
E∗
ω
ω
∗
Nominal active and reactive power of the inverter i [W,VAr]
Amplitude output voltage reference [V]
Angular frequency of the output voltage [rad/s]
Reference angular frequency [rad/s]
ωc
Cut-off angular frequency [rad/s]
ωo
Resonant frequency [rad/s]
Gp (s)
Compensator transfer function of Pc
Gq (s)
Compensator transfer function of Qc
mi
Integral phase droop coefficient [W − 1s]
mp
Proportional phase droop coefficient [W − 1]
md
Derivative phase droop coefficient [W − 1s− 1]
ni
Integral amplitude droop coefficient [Vs/VAr]
np
Derivative amplitude droop coefficient [V/VAr s]
nd
Derivative droop coefficient
pbc (s), qbc (s)
Active and reactive power small signal values
e Perturbed value of E
b
ζ
m, n
Damped coefficient
Proportional droop coefficients
kp
Proportional coefficient
ki
Integral coefficient
viii
Acronyms
ac
Alternating current
CSI
Current source inverter
dc
Direct current
DER
Distributed energy resource
DG
Distributed generation
DPGS
Distributed power generation systems
DSP
Digital signal processor
FLL
Frequency locked loop
IBS
Intelligent bypass switch
MPPT
Maximum power tracking point
PCC
Point of common coupling
PLL
Phase locked loop
PV
Photovoltaic
PWM
Pulse width modulation
SOGI
Second order generalized integrator
THD
Total harmonic distortion
UPS
Uninterruptible power supply
VSI
Voltage source inverter
ix
x
C ONTENTS
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1 Introduction
1
1.1
Smart-Grids using Distributed Energy Resources . . . . . . . . . . . .
1
1.2
Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3
Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2 State of the Art and Case Study Description
9
2.1
Microgrids as a new energetic paradigm . . . . . . . . . . . . . . . . .
9
2.2
Microgrid Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3
Microgrid operation modes . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1
Islanded operation mode of a Microgrid . . . . . . . . . . . . . 17
2.3.2
Transition between grid-connected and islanded mode . . . . . 18
2.4
Hierarchical control and management of Microgrids . . . . . . . . . . . 19
2.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
xi
3 Adaptive Droop Method
23
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2
Estimation of the Grid parameters . . . . . . . . . . . . . . . . . . . . 24
3.3
Droop method concept . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4
Adaptive Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1
Power flow analysis . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.2
Small signal modeling . . . . . . . . . . . . . . . . . . . . . . 30
3.5
Control Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.7
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.8
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Droop control method applied for voltage sag mitigation
45
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2
Voltage and frequency support . . . . . . . . . . . . . . . . . . . . . . 46
4.3
Multifunctional converter for voltage sags mitigation . . . . . . . . . . 48
4.4
Power stage configuration . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5
Control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6
System dynamics and control parameters design . . . . . . . . . . . . . 55
4.7
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.8
Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.9
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
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5 Hierarchical control for flexible Microgrids
71
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2
Microgrid structure and control . . . . . . . . . . . . . . . . . . . . . . 72
5.3
Primary Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4
Secondary Control Structure . . . . . . . . . . . . . . . . . . . . . . . 76
5.5
Islanded Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.6
Transitions Between Grid-Connected and Islanded Operation . . . . . . 78
5.7
Small-signal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.8
5.9
5.7.1
Primary Control Analysis . . . . . . . . . . . . . . . . . . . . 79
5.7.2
Secondary Control Analysis . . . . . . . . . . . . . . . . . . . 81
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.8.1
Harmonic-Current Sharing . . . . . . . . . . . . . . . . . . . . 82
5.8.2
Hot-Swap Operation . . . . . . . . . . . . . . . . . . . . . . . 84
5.8.3
Microgrid Operation and Transitions . . . . . . . . . . . . . . . 85
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6 Conclusions
6.1
95
Key Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.1.1
Journal Publications . . . . . . . . . . . . . . . . . . . . . . . 97
6.1.2
Conference Publications . . . . . . . . . . . . . . . . . . . . . 98
6.1.3
Book Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . 99
xiii
6.2
General Contributions of the Thesis . . . . . . . . . . . . . . . . . . . 99
6.3
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Bibliography
102
xiv
L IST
OF
TABLES
3.1
System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1
Power Stage and Control Parameters . . . . . . . . . . . . . . . . . . . 59
5.1
Control System Parameters . . . . . . . . . . . . . . . . . . . . . . . . 82
6.1
Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
xv
xvi
L IST
1.1
OF
F IGURES
A Microgrid based on renewable energy sources. (Courtesy of Mastervolt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2
a) Multiple layers of an inverter (Courtesy of Mastervolt). b) Basic
schematic diagram of a power stage of a single phase inverter. . . . . . 12
2.2
P − ω and Q − E grid scheme using P ∗ and Q∗ as setpoints. . . . . . . 13
2.3
Block diagram of a P/Q droop controller. . . . . . . . . . . . . . . . . . 14
2.4
Multi-loop control droop strategy with the virtual output impedance approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5
Hierarchical levels of a flexible Microgrid operations modes and transfer between modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6
Primary and secondary control based on hierarchical management strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7
Droop characteristic when supplying capacitive or inductive loads. . . . 21
2.8
Block diagram of the tertiary control and the synchronization control
loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1
Block diagram of the SOGI-FLL. . . . . . . . . . . . . . . . . . . . . . 25
3.2
Equivalent circuit of the VSI connected to the grid. . . . . . . . . . . . 25
3.3
V-I characteristic of the grid for a particular frequency. . . . . . . . . . 26
3.4
Block diagram of the grid parameters identification algorithm. . . . . . 27
xvii
3.5
Block diagram of the adaptive droop control. . . . . . . . . . . . . . . 30
3.6
Trace of root locus for 0.00005 < mp < 0.0001. . . . . . . . . . . . . . 33
3.7
Trace of root locus for 1x10−6 < mi < 4x10−5. . . . . . . . . . . . . . 33
3.8
Trace of root locus for 0.0004 < np < 0.01. . . . . . . . . . . . . . . . 34
3.9
Block diagram of the SOGI and the proposed adaptive droop control
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.10 Block diagram of the whole proposed controller using the synchronization control loops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.11 Variations of the grid impedance, R and L estimation. . . . . . . . . . . 37
3.12 Transient response of the system dynamics and the obtained model (18).
38
3.13 Start up of P for different line impedances, (a) without and (b) with the
estimation algorithm of Zg . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.14 Transition from islanding to grid-connected mode:(a) synchronization
process (grid and VSI voltages), (b) error between grid and inverter voltages, and (c) P and Q behavior in both operation modes. . . . . . . . . 40
3.15 Scheme of the experimental setup. . . . . . . . . . . . . . . . . . . . . 41
3.16 Panel supervisor of the ControlDesk from the dSPACE. . . . . . . . . . 41
3.17 Synchronization of the inverter to the grid: (a) voltage waveforms (b)
error between grid and inverter voltages. . . . . . . . . . . . . . . . . . 42
3.18 Active power transient response for Q = 0 V Ar from 0 to 1000W (P:
blue line, Q: black line). . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.19 Active power step change for Q = 0 V Ar (P: blue line, Q: black line). . 43
3.20 Reactive power transient response from 0 to -1000VAr for P= 0W. (P:
blue line, Q: black line). . . . . . . . . . . . . . . . . . . . . . . . . . 44
xviii
3.21 Power dynamic during transition from islanding to grid-connected mode. 44
4.1
Scheme of the power flow transfer through the utility grid. . . . . . . . 47
4.2
Graphical representation of the line impedance vectors. . . . . . . . . . 47
4.3
Equivalent circuit of the power stage of shunt converters: (a) Current
controlled. and (b) Voltage controlled. . . . . . . . . . . . . . . . . . . 49
4.4
Vector diagram of the shunt converter providing both active and reactive
power: (a) normal conditions; (b) voltage sag compensation of 0.15p.u.
4.5
49
Block-diagram of the grid-connected PV system power stage and its
control scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6
Relationship between the droop-based controller. . . . . . . . . . . . . 52
4.7
Power flow circuit in presence of a voltage dip. . . . . . . . . . . . . . 52
4.8
Power flow-based circuit modeling. a) Equivalent circuit b) General
approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.9
Block diagram of the droop control loops. . . . . . . . . . . . . . . . . 55
4.10 a) Root locus for 0.00002 < mp < 0.001 and mi = 0.0002. b) Root
locus for 0.000002 < mi < 0.0018 and mp = 0.00006. c) Root locus
diagram for grid inductance variations: 8.5mH < LG < 5000mH. . . . 58
4.11 Steady-state operation during grid normal condition: (a) Inverter current IC (b) Grid current IG , and (c) Load current IL . . . . . . . . . . . . 60
4.12 Active and reactive power transient responses and step changes provided by the PV inverter during normal operation. . . . . . . . . . . . . 61
4.13 Active and reactive power provided by the PV inverter in the presence
of a voltage sag of 0.15 p.u. . . . . . . . . . . . . . . . . . . . . . . . . 61
4.14 Current waveforms in case of a voltage sag of 0.15p.u. (inverter current
IC , grid current IG , and load current IL ). . . . . . . . . . . . . . . . . . 62
xix
4.15 Detail of the waveforms during the sag:
grid voltage (upper)
[100V/div], and grid current (lower) [10A/div]. . . . . . . . . . . . . . 62
4.16 Active and reactive power provided by the PV inverter in presence of a
voltage sag of 0.15p.u. when Pc∗ = 500W . . . . . . . . . . . . . . . . . 63
4.17 Current waveforms in case of a voltage sag of 0.15 p.u. (inverter current
IC (upper), load current IL (middle) and grid current IG (bottom) when
Pc∗ = 500W ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.18 Grid voltage waveform in presence of 1st, 3rd, 5th 7th and 9th voltage
harmonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.19 Active and reactive power transient responses and step changes provided by the PV inverter using the distorted grid waveform. . . . . . . . 64
4.20 Single-phase rectifier with R-C circuit as nonlinear load. . . . . . . . . 65
4.21 Inverter output voltage (detail), active and reactive power transient responses under a non-linear load. . . . . . . . . . . . . . . . . . . . . . 65
4.22 Current waveforms in case of a non-linear load and Vg with harmonics:
inverter current IC (upper), load current Il (middle), and grid current IG
(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.23 Laboratory Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.24 Experimental results in case of a voltage sag of 0.15 p.u. (voltage controlled inverter with droop control): 1) grid current [10V/div], 2) load
voltage [400 V/div], 3) grid voltage [400V/div]. . . . . . . . . . . . . . 68
4.25 Voltage waveforms during the sag [100V/div]: grid voltage (channel 4,
upper), capacitor voltage (channel 3, middle) and load voltage (channel
3, lower). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.26 Waveforms of the grid voltage (channel 4, upper) [100V/div], and the
grid current (channel 1, lower) [10A/div] during the sag. . . . . . . . . 69
xx
5.1
Typical structure of inverter Microgrid based on renewable energies. . . 73
5.2
Power flow control between the grid and the Microgrid. . . . . . . . . . 76
5.3
Droop characteristic as function of the battery charge level. . . . . . . . 77
5.4
Block diagram of the inverter control loops. . . . . . . . . . . . . . . . 79
5.5
Configuration setup for simulation results of the Microgrid. . . . . . . . 80
5.6
Root locus plot in function of the batteries charge level (arrows indicate
decreasing value from 1 to 0.01). . . . . . . . . . . . . . . . . . . . . . 81
5.7
Root locus plot for a) kp = 0.8 and 0.1 ≤ ki ≤ 0.8 b) ki = 0.5 and
0.7 ≤ kp ≤ 0.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.8
Harmonic decomposition extracted by using the (top) bank of bandpass
filters and (bottom) output currents of a two-UPS system with highly
unbalanced power lines, sharing a nonlinear load (a) without and (b)
with the harmonic-current sharing loop. . . . . . . . . . . . . . . . . . 84
5.9
Circulating current when a second UPS is connected at t = 0.8 (a)
without the soft start, (b) with the soft start LDo =80 µH, and (c) LDo =
800 µH (Y -axis:2A/div). . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.10 Output impedance ofUPS#2 and output currents of the UPS#1 and
UPS#2 in soft-start operation (TST =0.1s and LDo =80H). . . . . . . . . 87
5.11 Dynamic performance of two inverters using the hierarchical control
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.12 Active and reactive-power transients between grid-connected and islanded modes (Y-axis: P=1 kW/div, Q=1 kVAr/div). . . . . . . . . . . . 89
5.13 Active power dynamic during transients changes from grid-connected
and islanded modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.14 Dynamic performance of the output currents when sharing a pure 40F
capacitive load. (a) Connection. (b) Disconnection (Y -axis: 4 A/div). . 90
xxi
5.15 Output currents of the UPS#1, UPS#2, UPS#3, and UPS#4 in a)
soft-start operation (TST =0.1s and LDo = 80mH) and b) disconnection
scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.16 Steady state of the output currents when sharing a pure 40µF capacitive
load (X-axis:10 ms/div; Y -axis: 5 A/div). . . . . . . . . . . . . . . . . 91
5.17 Transient response of the output currents and the circulating current (Xaxis: 50 ms/div; Y -axis: 20 A/div). . . . . . . . . . . . . . . . . . . . 92
5.18 Waveforms of the parallel system sharing a nonlinear load. Output voltage and load current (X-axis: 5 ms, Y -axis: 20 A/div). . . . . . . . . . 92
xxii
C HAPTER 1
I NTRODUCTION
Renewable energy emerges as an alternative way of generating clean energy. As a
result, increasing the use of ’green’ energy benefits the global environment, making
it a global concern. This topic relies on a variety of manufacturing and installation
industries for its development. As a solution, continuously small and smart grid energy
systems appear including renewable energy resources, microgenerators, small energy
storage systems, critical and noncritical loads, forming among them a special type of
distributed generation system called the Microgrid.
Microgrids concerns issues like energy management, system stability, voltage quality, active and reactive power flow control, islanding detection, grid synchronization,
and system recovery. All this, making optimal use of small scale energy generation
interacting together, increasing the use of renewable energy sources, and operating in
grid connected or in autonomous mode. These small but smart grids present a new
paradigm for low voltage distribution systems, in which a multilevel control system
must be performed in order to ensure the proper operation of the Microgrid.
1.1 Smart-Grids using Distributed Energy Resources
The smart grid as part of a Microgrid increases the integration of technologies that allows to regard electric grid operations and design. Also, this small but smart grid will
1
Chapter 1 : Introduction
2
Figure 1.1: A Microgrid based on renewable energy sources.
(Courtesy of Mastervolt).
use advanced technology to transform the energy production and power distribution system into a more intelligent, reliable, self-balancing, and interactive network that enables
enhanced environmental stewardship, operational efficiencies, and energy security. The
debate over what constitutes a smart grid is still emerging. A smart power grid refers
to a ”vision” of a power distribution network that will see upgrades made on long distance power transmission lines and grids to both optimize current operations, as well as
open up new markets to alternative energy. This allows more power to travel with less
resistance to further reaches of markets (cities, towns, rural areas, etc).
Recent advances using smart grids to maximize operations efficiency, monitoring
and supervisory control, power management, and utility grid supplying, make this kind
of systems a suitable solution for decentralizing the electricity production. Thus, the
study of this small grids is imperative because they are helpful to fulfill the maximization of the following issues:
⊲ Efficiency and demand trends involving technological changes.
⊲ Advanced energy storage systems.
1.1 : Smart-Grids using Distributed Energy Resources
3
⊲ Reduced system restoration time due to transitions between the utility grid and
the smart grid, improving network reliability.
⊲ Increased integration of distributed generation resources.
⊲ Increased security and tolerance to faults.
⊲ Power quality and system reliability.
⊲ Decentralized Power Management: how to generate an amount of power in a lot
of places, rather than a lot of power in one place.
A smart grid will use digital technology to allow two-way communication between
electricity generators and customers. It will, allow appliances in homes to use electricity
when it is abundant and inexpensive. It will allow electricity managers to peer into their
systems to identify problems and avoid them. In addition, it will provide rapid information about blackouts and power quality. These facts leads to integrate technologies that
can detect emerging problems through extensive measurements, fast communications,
centralized advanced diagnostics, and feedback control that quickly return the system
to a stable state behavior after interruptions or disturbances are presented.
Finally, because a smart grid is a complex system and contains many interdependent
technologies and strategies, is imperative to know the difficulty of to control it in order
to warranty both quality of supply and ensuring power management supervising critical
and non-critical loads. Also, the basic issue on small grids is the control of the number
of microsources. Microgrid concept allows larger distribution generation by placing
many microsources behind singles interfaces to the utility grid. Some key power system concepts based on power vs. frequency droops methodology, voltage control and
hierarchical control levels can be applied to improve system stability, enhance active
and reactive support, ride through capability, among others.
Chapter 1 : Introduction
4
1.2 Thesis Objectives
The main aim of this thesis is to solve problems related to the modeling, control, and
power management of distributed generation (DG) systems based on the Microgrid operating modes. After an introductive description of the Microgrid paradigm, some of
the control objectives related to DG systems starting from a single DG unit to a number
of interconnected units forming a Microgrid, will be solved. The research methodology
will be developed as follows:
⊲ Develop the system modeling based on the variables useful for an optimal control
of active and reactive power flows. The use of voltage source inverters (VSI)
as electronic interface with the Microgrid, needs for new analysis tools. As a
primary goal, an accurate model derived from the electrical scheme of a grid
interactive VSI system is demanded. The control variables of such VSIs will be
the amplitude, frequency and phase of the output voltage.
⊲ Analyze how to perform an accurate power flow control during transients, using
an active and reactive power decoupling control algorithm to make the system
independent from grid parameters.
⊲ Analyze and develop a virtual output impedance scheme solving the output
impedance of the inverter and its impact on the power sharing. The virtual output
impedance can be regarded as a new control variable. It can be helpful for special
functionalities like: nonlinear voltage supply, seamlessly connection (hot swap
operation), adaptive control laws, among others.
⊲ Realize the corresponding control laws based on a decentralized control methodology (droop functions) to improve system stability and dynamic performance,being able to share power with the grid in function of its nominal power.
⊲ Develop closed loop stability analysis, such as small-signal dynamics, frequency
domain behavior, pole dominance, or root locus diagrams, in order to obtain the
desired transient response that allows choosing the loop control parameters properly.
1.3 : Outline of the Thesis
5
Finally, the performance validation of the proposal control through experimental results
will be realized finding solutions to the following problems:
⊲ In grid-connected mode: Power injection accuracy due to sensitivity to the grid
parameters: line-impedance imbalance, amplitude and frequency.
⊲ In islanded mode: Power sharing accuracy due to the power line mismatches.
Further aspects will be studied about how to deal with utility failures, as well
as the frequency and amplitude regulation based on different levels of modeling,
control, and analysis.
⊲ Transition between grid connected and islanded operation: Synchronization and
system restoration process when a grid fault is cleared.
⊲ Voltage and frequency deviations inherent to the conventional droop methodology. Since it is not desirable to operate the system in a much lower frequency, a
complementary frequency restoration strategy must be imposed.
⊲ Reduction of grid voltage sag and harmonic distortion of the output voltage when
supplying linear and non-linear loads.
1.3 Outline of the Thesis
This thesis is organized in 6 chapters, as follows:
Chapter 2 introduces a survey of past work focusing on distributed generation of
electrical power, power management, control, and modes of operation in flexible Microgrids. The development of this chapter is developed based on the following reference,
⊲ Josep M. Guerrero and Juan. C. Vasquez, Uninterruptible Power Supplies, The
Industrial Electronics Handbook, Second edition, Irwin, J. David (ed.).
Chapter 3 considers the modeling principles, power flow analysis, small signal analysis based on a estimation of the grid parameters algorithm and finally a control structure using novel adaptive droop strategy which is explained and discussed. Equally, the
Chapter 1 : Introduction
6
case-study corresponds to a voltage source inverter (VSI) capable of operating in both
connected and islanded modes, as well as to transfer between these modes, seamlessly.
The development of this chapter is developed based on the following references,
⊲ J. C. Vasquez, J. M. Guerrero, A. Luna, P. Rodriguez, R. Teodorescu, Adaptive
Droop Control Applied to Voltage Source Inverters Operating in Grid-Connected
and Islanded modes, (Forthcoming to be included in IEEE Transactions on Industrial Electronics (T-IE)).
⊲ J. C. Vasquez, J. M. Guerrero, E. Gregorio, P. Rodriguez, R. Teodorescu and F.
Blaabjerg, Adaptive Droop Control Applied to Distributed Generation Inverters
Connected to the Grid, IEEE International Symposium on Industrial Electronics
(ISIE’08). Pages 2420-2425. Dec. 18, 2008.
Based on the control strategy proposed in chapter 3, chapter 4 is focused on a single
phase multifunctional inverter allowing the obtainment of voltage dip compensation
to the system and providing voltage ride-through capability applied to local loads. A
model and system stability analysis is given to properly choose the control parameters.
The development of this chapter is developed based on the following references,
⊲ Juan C. Vasquez, Rosa A. Mastromauro, Josep M. Guerrero, and Marco Liserre, Voltage Support Provided by a Droop-Controlled Multifunctional Inverter,
(Forthcoming to be included in IEEE Transactions on Industrial Electronics (TIE)).
⊲ R. A. Mastromauro, M. Liserre, A. dell’Aquila, J. M. Guerrero and J. C. Vasquez,
Droop Control of a Multifunctional PV Inverter. IEEE International Symposium
on Industrial Electronics (ISIE’08), pages 2396-2400. Dec. 18, 2008.
⊲ J. Matas, P. Rodriguez, J. M. Guerrero, J. C. Vasquez, Ride-Through Improvement
of Wind-Turbines Via Feedback Linearization, In IEEE International Symposium
on Industrial Electronics (ISIE’08), Pages 2377-2382, Dec. 18, 2008.
In chapter 5, a control strategy for a flexible Microgrid is presented. The Microgrid presented consists of several line-interactive uninterruptible power supply (UPS)
1.3 : Outline of the Thesis
7
systems. The control technique is based on the droop method to avoid critical communications among UPS units. Also, a control technique applied to a flexible Microgrid
capable of operating in either grid-connected or islanded mode importing/exporting
energy from/to the grid, is obtained. A small-signal analysis is presented in order to
analyze the system stability, which gives the rules to design the main control parameters. The hierarchical control concept is extended and explained for an AC Microgrid
based on a voltage and current regulation loops, an intermediate virtual impedance loop
and an outer power sharing loop. Microgrid operation and transitions, harmonic current
sharing and hot-swap operation topics are detailed as well. The development of this
chapter is developed based on the following references,
⊲ J. M. Guerrero, J. C. Vasquez, J. Matas, J. L. Sosa and L. Garcia de Vicuña.
Control Strategy for Flexible Microgrid Based on Parallel Line-Interactive UPS
Systems, IEEE Transactions on Industrial Electronics, Vol. 56, pages 726-736.
March 2009.
⊲ J. M. Guerrero, J. C. Vasquez, J. Matas, J. L. Sosa and L. Garcia de Vicuña, Parallel Operation of Uninterruptible Power Supply Systems in Microgrids, 12th European Conference on Power Electronics and Applications (EPE’07), sept.2007.
⊲ Josep M. Guerrero and Juan. C. Vasquez, Uninterruptible Power Supplies, The
Industrial Electronics Handbook, Second edition, Irwin, J. David (ed.).
Chapter 6 serves as a conclusion for this thesis point out all the contributions made
and the ways for future trends in Microgrids researching are discussed.
8
Chapter 1 : Introduction
C HAPTER 2
S TATE
OF THE
A RT
AND
C ASE S TUDY
D ESCRIPTION
2.1 Microgrids as a new energetic paradigm
In recent years, distributed generation of electrical power integrating renewable and
non-conventional energy resources has become a reality. Relevant issues such as energy
management, new control strategies for power electronic converters in the system, and
the detection and management of the Microgrid operation modes are considered in this
topic. To achieve efficient and safe operation of these systems in this new scenario, it
is necessary to carry out research at different levels in order to get a better use of the
energy sources.
First, most recent research works show the technical difficulty of efficiently controlling the Microgrid as a complete system. Second, energy management includes topics
like power electrical quality, protections, energy delivery to the loads, and flexible operation that allows the Microgrid to work in grid connected or islanded modes. This
line of research addresses all these questions, aiming at a rigorous study of this complex problem by using appropriate models of the parts that constitute the system, and
by introducing a methodology for the design of the control algorithms based on linear
adaptive control and nonlinear control techniques.
Another new concept is becoming one of the solutions to the power crisis: DG also
9
10
Chapter 2 : State of the Art and Case Study Description
called micro generation in the origin. DG of electric energy has become part of the
current electric power system; it consists of generating electrical power near the consumption area [47, 49–51], breaking with the traditional concept, in which generation
and consumption areas are far away from each other. The future of power supply system will be composed by a great quantity of low voltage Microgrids interconnected
through the distribution and transportation systems. Moreover, energy and ecological
issues such as the oil crisis, climate change and the high power supply demand around
the world have increased the need of new energy alternatives. In this context a new scenario is arising in small energy sources make up a new supply system: the Microgrid.
The use of this kind of power supply sources would not only assure its quality and its
opportune supply, but also a more efficient use of the natural resources. Likewise, the
amount of DG sources directly connected to the distribution network will be increased
actively [83]. The profits associated to the Microgrid concept are clear. On one hand,
an improvement of the efficiency in energy transportation (reduction of energy losses)
is achieved, when it is brought near the generation and consumption points. On the
other hand, the electricity generation with low or null emissions of CO2 and SO2 to
the atmosphere is possible, achieving a more responsible use of the available natural
resources. A last but not least important merit of Microgrids comes from the inherent
redundancy of generation systems, a fact that predicts that future power systems will be
more robust and safer from eventual faults in the electrical supply system.
In recent last years, different Microgrids management structures have been proposed. In these proposed structures, various aspects of that question have been outlined, but few works address the problem in all its extension [48]. Most recent research
projects show the technical difficulty of controlling the operation of Microgrid, because
they are complex systems in which several subsystems interact: energy sources, power
electronic converters, energy storage systems, loads and the grid. Among the goals of
this line of research, all the above subjects will be studied in the case of a Microgrid
that is capable of operating both isolated (autonomous) and seamlessly connected to the
utility main (grid-connected mode) [42, 43]. The implications for the control of the Microgrid derived from the transition between both operation modes will be considered.
Important contributions are expected about the control of power electronic converters
operating in Microgrids, as well as about the power system management.
2.2 : Microgrid Control
11
Further questions of special interest in the environment of distributed generation
and of Microgrids to which a strong research effort has been dedicated, are:
⊲ Synchronization techniques with the grid, such as phase locked loops, and network estimators that allow the calculation of the grid phase from the measurement
of the supply voltages. The correct synchronization under imperfect conditions
(imbalances, notches, distortion, etc.) is one of the key problems described in the
related literature. In the case of systems working in parallel, particularly in grid
isolated systems, the use of synchronization techniques among parallel modules
is also required, achieving an equal distribution of the power delivered by each
module.
⊲ The reduction of circulating currents among parallel connected modules [30].
The parallel connection of converters is a highly complex problem both in the case
of network connected systems and in isolated systems. With inadequate control
algorithms, important currents can appear circulating among the power converters
without arriving to the loads, overloading the generation capacity in a useless
way. Moreover, because is necessary to warrant some reliability and stability
among these modules, an extended control strategy analysis within literature has
been proposed [17, 44, 78, 81]. With some inadequate control algorithms, some
relevant currents among the converters (without reaching the loads) could arise
overcharging the generation capability, pointlessly.
2.2 Microgrid Control
An experimental Microgrid is based on small wind generator, photovoltaic sources,
energy storage systems and among others, and the overall system and the model approximation consist of several modules: the utility grid power, inverters and loads.
A simple inverter is essentially integrated with a dc power source and a full bridge
and an L−C output filter [56] as shown in Figure 2.1. In this stage, inverter management and control will be addressed. Moreover, inverters can be individually modelated,
and its operation frequency can be configured by means of its local controller, which
includes the dynamic of the controller, the output filter, and the voltage and current
Chapter 2 : State of the Art and Case Study Description
12
a)
b)
Figure 2.1: a) Multiple layers of an inverter (Courtesy of
Mastervolt). b) Basic schematic diagram of a power
stage of a single phase inverter.
control loops [38, 46, 69]. In the same way, parallel inverter operation has a lot of advantages, both economic and in terms of equipment maintenance in comparison to a
simple inverter. However, the circulating current through them could produce damage
in some semiconductors. That is why, a well-designed parallel inverter system not only
provides the means for an excellent current distribution, but also, a high viability, modularity, easy-maintenance and flexibility [89]. Two or more parallel inverters are subject
to the following restrictions:
⊲ All the parallel inverters must operate synchronously.
⊲ All the inverter output voltages must have the same amplitude, frequency and
phase.
⊲ The inverters output current needs to be distributed according to their nominal
power.
Each inverter will have a external power loop based on droop control [21–23,36,63,
81, 84], called also as autonomous or decentralized control, whose purpose is to share
active and reactive power among DG units and to improve the system performance and
2.2 : Microgrid Control
ω
13
ω = ω − m(P-P*)
E = E *− n(Q-Q*)
E
ω∗
E*
P
P*
Q*
Q
Figure 2.2: P − ω and Q − E grid scheme using P ∗ and Q∗ as
setpoints.
stability, adjusting at the same time both the frequency and the magnitude of the output
voltage. The droop control scheme, can be expressed as follows
ω = ω ∗ − m · (P − P ∗),
(2.1)
E = E ∗ − n · (Q − Q∗ ),
(2.2)
where ω and E ∗ are the frequency and the amplitude of the output voltage. m and
n coefficients define the corresponding slopes. P ∗ and Q∗ are the active and reactive
power references, which are commonly set to zero when we connect UPS units in parallel autonomously, forming energetic island. However, if we want to share power with
a constant power source, e.g. the utility grid, is necessary to fix both active and reactive power source to be drawn from the unit. This droop method increases the system
performance due to the autonomous operation among the modules. This way, the amplitude and frequency output voltage can be influenced by the current sharing through a
self-regulation mechanism that uses both the active and reactive local power from each
unit [59], [82].
In order to obtain good power sharing, the frequency and amplitude output voltage
must be fine-tuned in the control loop, with the aim of compensating active and reactive
power imbalance [66], [54]. This concept is derived from the classic high power system
theory, in which generator frequency decreases when the grid utility power is increased
[26], [9]. To implement the droop method, equations 2.1 and 2.2, can be used, keeping
Chapter 2 : State of the Art and Case Study Description
14
Q−
Io
LPF
+
n
Droop
Controller
+
E*
Q*
+90º
−
E
φ
Vo
LPF
Power Calculation
P−
+
m
V o*=E sin(ω⋅t-φ)
Vo*
P*
Figure 2.3: Block diagram of a P/Q droop controller.
in mind that active and reactive power must be measured and averaged with a running
average window over one cycle of the fundamental frequency, so that the powers are
evaluated at fundamental frequency. This operation can be implemented by means of
low-pass filters with a reduced bandwidth. Furthermore, the filters that calculate the
mean values both the active and reactive power and the coefficients of the slopes, are
strong determinants of the system dynamic and performance, especially in paralleled
power supplies. The oscillating phenomena due to the phase difference among modules
could produce some instability, and a high circulating transient current could overcharge
the system and equipment as well.
In transmission systems, the grid impedance is mainly inductive; This is the reason
why it is used to adopt P − ω and Q − E slopes. Hence, the inverter can inject desired
active and reactive power to the main grid, regulating the output voltage and responding
to some linear load changes. The inverter inner control will include voltage and current
controllers, which will be designed in order to reject high frequency disturbances and
absorbing the output L − C filter to avoid any resonant signal with the main grid. Considering droop method, a compromise between both frequency and voltage regulation
as active and reactive power equalization can exist. In other words, if the droop slope
coefficients are increased is possible to obtain good power equalization, even though
regulation could be compromised. In practice, these deviations are acceptable if for
instance, they are less of 2% in frequency and 5% in amplitude.
2.2 : Microgrid Control
ω
E
Voltage
Reference Vo*
E sin (wt)
15
v
+
Voltage
loop
−
Current
loop
PWM + UPS
Inverter
i
Z o (s)
Droop control
Q
ω = ω * − mP
Virtual Impedance
loop
P&Q
Calculation
P
E = E * − nQ
Figure 2.4: Multi-loop control droop strategy with the virtual output
impedance approach.
One of the primary aspects in Microgrids control field in order to synchronize an
inverter output is using a phase-locked loop (PLL). However, one inconvenience of this
scheme is the poor dynamic response, and a small phase error among the inverters,
causing high circulating current between them. Moreover, if the output voltage of each
inverter had the same amplitude, frequency and phase, in theory the load current would
be shared equally. In practice, due to the component tolerance and the wrong adjustment of the line impedance, the load current not be shared in an optimal form, resulting
in circulating current among the inverters overloading the overall system. From these
inconveniences, different methods in literature have been developed, such as the multiloop control strategies, shown in Figure 2.4. This scheme is composed of an external
loop whose function is to regulate the output voltage, whereas the inner loop supervises
the inductor current [55,90,91] or the capacitor current [19,29,74] of the output filter in
order to reach a fast dynamic response. This control diagram provides a high viability
in parameters design and a Low Total Harmonic Distortion (THD), but it requires both
complex analysis and a parameter synchronization algorithm. Similarly, another relevant aspect to provide proper output impedance is the virtual output impedance loop.
Chapter 2 : State of the Art and Case Study Description
16
2.3 Microgrid operation modes
The Microgrid energy management must be performed by considering the energy storage systems and the control of the energy flows in both operation modes (with and
without connection to the public grid). In this sense, the Microgrid must be capable
of exporting/importing energy from/to the main grid, to control the active and reactive
power flow, and to supervise the energy storage [68]. In grid-connected mode, some of
the system dynamics are supplied by the utility grid due to the small size of the micro
sources. In islanded mode, system dynamic is depicted by its own micro sources, its
power regulation control and finally the main grid. Also, a small deviation from the
nominal frequency could be noticed. As a result, the storage unit will support all power
deviations by injecting or absorbing some active power proportionally to the frequency
deviation.
Likewise, most of the Microgrids are not designed in order to have a direct link with
the low voltage grid due to the characteristics of the power produced; hence, some electronic interfaces are required such as dc/ac or ac/dc/ac converters. Another problem is
the slow response at the control signals when a change of the output power occurs. The
absence of synchronous machines connected to the low-voltage power grid requires that
power balancing during the transient must be provided for power storage devices such
as batteries or flywheels. After some equipment faults and a power supply shutdown in
a conventional power system, some restoration difficulties could be produced, therefore,
as a Microgrid starting point; it must always be supplied by a local generation power
grid. In addition, the Microgrid should start correctly even though a power supply is
not present (blackstart).
When a power supply shutdown occurs, restoration process must be reduced as
much as possible in order to ensure a high reliability level. The restoration stages are
aimed at the plant restart, power generation of the main grid, and system frequency
synchronization. During this stage, some details must be considered such as the reactive power balance, commutation of the transient voltages, balancing power generation,
starting sequence, and coordination of the generation units. Thanks to its flexibility,
Microgrids restoration process is simpler due to the number of controller variables to
2.3 : Microgrid operation modes
17
be manipulated (switch, micro sources, and loads). When the Microgrid is again in
grid-connected operation mode, the main utility grid will provide both active and reactive power requirements as to ensure its operation frequency [8]. In this operation
mode, all the distributed generation units must supply the specified power, e.g. to minimize the power importing from the grid (peak shaving), whose requirements depend
on the global system, which vary from one system to the other. In addition, each distributed generation unit can be controlled through voltage regulation for active and reactive power generation using a communication bus. Typically, depending of the custom
desire, when the Microgrid is in grid-connected mode, both main grid and the local
micro sources send all the power to the loads. Hence, if any events in main grid are
presented, such as voltage dips or general faults, among others, islanded operation must
be started.
2.3.1 Islanded operation mode of a Microgrid
Microgrid autonomous mode is realized taking into account the static bypass switch
(IBS) opening [36] itself as a controllable load or source. Therefore, when the Microgrid is in islanded operation mode, the micro sources that feed the system are responsible for nominal voltage and frequency stability when power is shared by the generation
units. It is important to avoid overload the inverters and to ensure that load changes are
controlled in a proper form. Some control techniques which are based on communication links as master-slave scheme by can be adopted in systems where micro sources are
connected through a common bus or being close enough. However, a communication
link through a low-bandwidth system can be more economic, more reliable and finally,
attractive. Equally, in autonomous mode the Microgrid must satisfy the following issues:
⊲ Voltage and frequency management: The primary purpose is to balance the system against losses and system disturbances so that the desired frequency and
power interchange is maintained. that is why, voltage and frequency inner loops
must be adjusted and regulated as reference within acceptable limits.
18
Chapter 2 : State of the Art and Case Study Description
⊲ Supply and demand balancing: when the system is importing from the grid before islanding, the resulting frequency is smaller than the main frequency, been
possible that one of the units reaches maximum power in autonomous operation.
Besides, the droop characteristic slope tries to switch in vertical as soon as the
maximum power limit has been reached and the operating point moves downward vertically as load increases. In the opposite case, when the unit is exporting
and the new frequency is larger than nominal.
⊲ Power quality: power quality must synthesize quality of supply and quality of
consumption using sustainable development as transporting of renewable energy,
embedded generation, using high requirements on quality and reliability by industrial, commercial and domestic loads/costumers avoiding variations as harmonic
distortion or sudden events as interruptions or even voltage dips.
Also, when the Microgrid is operating in islanded mode all the micro sources are
constant power sources, injecting the desired power towards the utility grid. At the same
time, the micro sources are controlled in order to provide all the load voltage while
frequency is kept within the allowed limits. Islanded operation mode of a Microgrid
can be started because of two main reasons: first, a non-intentioned form in order to do
maintenance or economical criterion. Second, due to main utility grid faults for nonintentionally causes. The interrupting time of the power supply can be reduced using
this method until the grid utility service is disposed again.
2.3.2 Transition between grid-connected and islanded mode
As commented above, the IBS is continuously supervising both the utility grid and the
Microgrid status is depicted in the figure 2.5. When a fault in the main grid has been
detected by the IBS, it must disconnect the Microgrid. In such a case, this switch can
readjust the power reference at nominal values, although it is not strictly necessary. In
addition to this, if maximum permissible deviation is not exceeded, (typically, 2% for
frequency and 5% amplitude) the voltage amplitude and frequency can be measured
inside the Microgrid, and operation points (P ∗ and Q∗ ) avoids the frequency deviation
and amplitude of the droop method. When the Microgrid is in islanded mode operation,
2.4 : Hierarchical control and management of Microgrids
19
Bypass off
P*
E= V*
ω=ω*
Q=Q*
P= ;
Import/export
P/Q
Grid
Connected
Islanding
Operation
E= Vg
Bypass on
ω=ωg
Figure 2.5: Hierarchical levels of a flexible Microgrid operations
modes and transfer between modes.
and IBS detects main grid fault-free stability, synchronization among voltage, amplitude, phase and frequency must be realized for connecting operation. Hence, amplitude
is adjusted through small steps in Q∗ , and both frequency and phase are adjusted by
means of small steps P ∗ proportionally to phase error between the Microgrid and the
utility grid.
2.4 Hierarchical control and management of Microgrids
Functionally, the Microgrid (as a grid) must operate within three control hierarchical
levels:
Primary Control : P/Q Droop Control.
As a control main loop, inverters are programmed to act as generators by including
virtual inertias by means of the droop method. It specifically adjusts the frequency or
amplitude output voltage as a function of the desired active and reactive power. Thus,
active and reactive power can be shared equally among the inverters. For reliability
and to ensure local stability, voltage regulation is needed. Without this supervision
control, most of the micro sources can present reactive power and operation voltage
oscillations. To avoid this fact, high circulating currents among the sources must be
eliminated through the voltage control, in such a way that reactive power generation
Chapter 2 : State of the Art and Case Study Description
20
Frequency restoration level
ωref
Gwr(s)
ωο
Vref
Gvr(s)
Vo
ω=ω*-m(P*-P)
Ε=Ε*-n(Q*-Q)
δω Droop
control
and
δV Sine
generator
ω
Ε
Current
control
loop
Voltage
control
loop
Inner
loops
Driver and
PWM
Generator
io
v
Virtual
Impedance loop
Voltage restoration level
Secondary control
Low bandwidth
communications
P/Q
calculation
Primary control
Outer
loops
Figure 2.6: Primary and secondary control based on hierarchical
management strategy.
of the micro source be more capacitive, reducing the voltage set point value. In other
words, while Q is a high inductive value, the voltage reference value will be increased
as Figure 2.7 shows.
Secondary control: Frequency-Voltage Restoration and Synchronization.
In order to restore the Microgrid voltage to nominal values, supervisor system must
send the corresponding signals using low-bandwidth communication. Also, this control
can be used for Microgrid synchronization to the main grid before performing the interconnection, transiting from islanded to grid-connected mode. The power distribution
through the control stage is based on a static relationship between f and P, and it is
implemented as a droop scheme. Likewise, frequency and voltage restoration to their
nominal values must be adjusted when a load change is realized. Originally, frequency
deviation from the nominal measured frequency grid brings to a integrator implementation [16]. For some parallel sources, this displacement can not be produced equally
due to measured errors. In addition, if the power sources are connected in islanded
mode through the main grid at different times, the load behavior can not be completely
ensured because all the initial conditions (Historical) from the integrators, are different.
Tertiary control: P/Q Import and Export.
2.5 : Conclusions
21
ω
E
ω*
∆ω
ω = ω * − mP
∆E
E*
E = E * −nQ
Capacitive load
P
Pnom
−Qnom
Inductive load
Q
Qnom
Figure 2.7: Droop characteristic when supplying capacitive or
inductive loads.
In the third control hierarchy, the adjustment of the inverters references connected to
the Microgrid and even of the generators maximum power point trackers is performed,
so that the energy flows are optimized. The set points of the Microgrid inverters can be
adjusted, in order to control the power flow, in global (the Microgrid imports/exports
energy) or local terms (hierarchy of spending energy). Normally, power flow depends
on economic issues. Economic data must be processed and used to make decisions
in the Microgrid. Each controller must respond autonomously to the system changes
without requiring load data, the IBS or other sources. Thus, the controller uses a power
and voltage feedback control based on the real-time measured values of both P , Q,
frequency and ac voltage to generate the desired voltage amplitude and phase angle by
means of the droop control.
2.5 Conclusions
This chapter exposes Microgrids field as a multidisciplinary area, which encompasses
power stage topologies, control techniques, technological storage solutions, and complex power systems, among others. Hence, Microgrids are becoming a reality in a scenario in which renewable energy and distributed storage systems can be conjugated and
also integrated into the grid. These concepts are becoming more important due to not
only environmental aspects, but also social, economic, and political interests. Equally,
Chapter 2 : State of the Art and Case Study Description
22
IBS
Main AC grid
Microgrid
P,Q
PLL
P/Q
calculation
RMS
δφ
Q
Q* +
P* +
_
Vref
Gq
_
P
+
Gp
_
Gse
δφ
φref
Tertiary control
+
δv
+
+
Secondary control
Gsw
δω
Synchronization loop
Figure 2.8: Block diagram of the tertiary control and the
synchronization control loop.
DG concept is pointing out that the future utility line will be formed by distributed energy resources and small grids (minigrids or Microgrids) interconnected between them.
In fact, the responsibility of the final user is the production and storage part of the
electrical power of the whole system.
C HAPTER 3
A DAPTIVE D ROOP M ETHOD
3.1 Introduction
DG systems and Microgrids are becoming more and more important when trying to increase the renewable energy penetration. In this sense, the use of intelligent power interfaces between the electrical generation sources and the grid is mandatory. These interfaces have a final stage consisting of dc/ac inverters, which can be classified in currentsource inverters (CSI) and voltage-source inverters (VSI). In order to inject current to
the grid, CSI are commonly used, while in island or autonomous operation, VSI are
needed to maintain the voltage stable [86]. VSIs are relevant for DG applications since
they do not need any external reference to stay synchronized [45], [14]. In fact, they can
operate in parallel with other inverters by using frequency and voltage droops, forming
autonomous or isolated Microgrids [8]. Also, VSIs are convenient since they can provide to distributed power generation system performances like ride-through capability
and power quality enhancement [85], [76], [93], [87], [24], [88], [53], [79], [35]. When
these inverters are required to operate in grid-connected mode, they often change their
behavior from voltage to current sources [80].
Nevertheless, to achieve flexible Microgrids, i.e. to be able to operate in both gridconnected and islanded modes, VSIs are required to control the exported or imported
power to the main grid and to stabilize the Microgrid [36], [70]. In this sense, the
droop method can be used to inject active and reactive power from the VSI to the grid
23
Chapter 3 : Adaptive Droop Method
24
by adjusting the frequency and amplitude of the output voltage [8, 14, 45]. However,
in order to independently control the active and reactive power flows, the conventional
droop method needs some knowledge of some parameters of the grid. In this sense, the
estimation of the grid impedance can be useful not only for injecting P and Q into the
grid with high precision, but also for islanding detection.
In this chapter, we propose a control scheme based on the droop method which
automatically adjusts their parameters by using a grid impedance estimation method
based on analyzing the voltage and current variations at the point of common coupling
(PCC) resulting from small deviations in the power generated by the VSI [84]. The VSI
is able to operate in both grid-connected and islanded modes, as well as to seamlessly
transfer between these modes.
3.2 Estimation of the Grid parameters
The grid characterization technique used is based on processing the voltage and current phasors at the PCC between the power converter and the grid. A frequency locked
loop based on the second order generalized integrator (SOGI-FLL) is used to monitor
such voltage and current phasors. As Figure 3.1 shows, two cascaded integrators working in closed loop are used to implement the SOGI [92], [84]. This grid monitoring
technique provides high precision, low computational cost and frequency adaptation
capability [73], [72]. The aforementioned SOGI-FLL is also applied to monitoring the
−
→
current injected into the PCC in order to obtain the current phasor I = id + jia . The
SOGI-FLL acts as a selective filter for detecting two in-quadrature output signals, being a very useful feature to attenuate harmonics on the monitored voltage and current
−
→
−
→
and to accurately detect the phasors of the grid voltage and current (Vg and Ig ) at the
fundamental grid frequency. The detected voltage and current in-quadrature signals are
projected on a d−q rotating reference frame to obtain coherent voltage and current phasors. The technique used for estimating the grid-parameters stems from a linear interpretation of the grid in which distributed power generators are connected to. Therefore,
the grid can be seen from the PCC of a power generator as a simple Thevenin circuit
3.2 : Estimation of the Grid parameters
εv
v
25
∫
k
ω′
SOGI -QSG
∫
v′
vq ′
vq ′
−1
FLL
εf
εv
γ
ω ff
∫
ω′
Figure 3.1: Block diagram of the SOGI-FLL.
V pcc
VSI
E ∠φ
E i pcc
Zo
Z g ∠θ g = Rg + jX L Vg ∠0º
Figure 3.2: Equivalent circuit of the VSI connected to the grid.
−
→
−
→
constituted by a grid impedance Zg and a header voltage Vg . Even though the v −i characteristic of the ac grid can not be represented by a simple two-dimensional Cartesian
plane, Figures 3.2 and 3.3 help to illustrate further explanations about the impedance
detection method used in this section since it depicts the relationship between voltage
and current phasors at the PCC for a particular frequency. From the measurement of
the voltage and current phasors at the PCC at two different operating points, linearity
in the v − i characteristic of Figure 3.3 allows writing (3.1) and (3.2) for estimating the
−
→
−
→
grid impedance Zg and the open circuit voltage Vg , respectively
−−→
−
→ −
→
−
→
△Vpcc
V1 − V2
Zg = Zg ∠θg = −→ = −
→ −
→,
△Ipcc
I1 − I2
−
→−
→ −
→−
→
−
→
−−−→ −
→−−−→ I1 V2 − I2 V1
Vg = Vg ∠φ = Vpcc(i) − Zg Ipcc(i) = −
→ −
→ ,
I1 − I2
(3.1)
(3.2)
Chapter 3 : Adaptive Droop Method
26
V pcc
(2)
∆V pcc
Vg
I sc
(1)
I pcc
∆ I pcc
Figure 3.3: V-I characteristic of the grid for a particular frequency.
where Zg and θg are the magnitude and the angle grid impedance, respectively. Several
techniques for detecting the grid impedance are either directly or indirectly based on this
basic principle [7,10,40,71,77]. In this work, the grid parameters are estimated from the
active and reactive power variations generated by a grid-connected converter in which
a droop-controller is implemented. The cornerstone of this estimation technique is the
accuracy in the on-line measurement of voltage and current phasors at the PCC, which
is performed based on the SOGI-FLL. Figure 3.4 shows the diagram of the algorithm
used in this work to identify the grid parameters. It is worth saying that the estimated
values of the angle and magnitude of the grid voltage impedance, and their voltage and
the frequency are transiently wrong after each change in the grid parameters. Therefore,
as shown in Figure 3.4, the FLL block is only implemented on the monitored voltage v
and the angle θ′ is calculated from the integration of the voltage frequency. As transient
values cannot be sent to the droop-controller of the VSI, a small buffer of three rows is
added at the output of the grid parameters identification block of Figure 3.4.
3.3 Droop method concept
With the aim of connecting several parallel inverters without control intercommunications, the droop method is often proposed [70]. The applications of such a kind of
control are typically industrial UPS systems [30] or islanding Microgrids [29], [33].
3.3 : Droop method concept
27
GRID
PARAMETERS
SOGI-QSG
ipcc
i′
i
Td q
 
iq ′
ω′
εi
id
iq
θ′
v
ω′
v′
vq ′
Td q
εv
vd
vq
ωg
θ′
∫
FLL
ω′
θg
Vg
SOGI-QSG
v p cc
Zg
vq′
ω ′s s
εv
ω′
Samp lin g
tri gg er
S &H
Figure 3.4: Block diagram of the grid parameters identification
algorithm.
The conventional droop method is based on the principle that the phase and the amplitude of the inverter can be used to control active and reactive-power flows [82]. Hence,
the conventional droop method can be expressed as follows:
ω = ω ∗ − m · P,
(3.3)
E = E ∗ − n · Q,
(3.4)
where E is the amplitude of the inverter output voltage; φ is the frequency of the inverter; ω ∗ and E ∗ are the frequency and amplitude at no-load, respectively; and m and
n are the proportional droop coefficients. The active and reactive powers flowing from
an inverter to a grid through an inductor can be expressed as follows [9]:
EVg cosφ Vg2
EVg
P =
−
cos θg +
sin φ sin θg ,
Zg
Zg
Zg
EVg cosφ Vg2
EVg
Q=
−
sin θg −
sin φ sin θg ,
Zg
Zg
Zg
(3.5)
(3.6)
where Z and θ are the magnitude and the phase of the output impedance, respectively;
V is the common bus voltage; and φ is the phase angle between the inverter output and
the Microgrid voltages. Notice that there is no decoupling between P − ω and Q − E.
Chapter 3 : Adaptive Droop Method
28
However, it is very important to keep in mind that the droop method is based on two
main assumptions.
Assumption 1:The output impedance is purely inductive, and Zg = X and ω = 90o
with 3.5 and 3.6 become
EVg
sin φ,
X
Vg2
EVg
Q=
cos φ −
.
X
X
P =
(3.7)
(3.8)
This is often justified due to the large inductor of the filter inverter and to the impedance
of the power lines. However, the inverter output impedance depends on the control
loops, and the impedance of the power lines is mainly resistive in low voltage applications. This problem can be overcome by adding an output inductor, resulting in an LCL
output filter, or by programming a virtual output impedance through a control loop.
Assumption 2: The angle φ is small; we can derive that sin φ ≈ φ and cos φ ≈ 1,
and consequently,
EVg
φ,
X
Vg
Q ≈ (E − Vg ).
X
P ≈
(3.9)
(3.10)
Note that, taking these considerations into account, P and Q are linearly dependent
on ω and E. This approximation is true if the output impedance is not too large,
as in most practical cases. In the droop method, each unit uses frequency instead of
phase to control the active-power flows, considering that they do not know the initial
phase value of the other units. However, the initial frequency at no load can be easily fixed as φ . As a consequence, the droop method has an inherent tradeoff between
the active-power sharing and the frequency accuracy, thus resulting in frequency deviations. In [15], frequency restoration loops were proposed to eliminate these frequency
deviations. However, in general, it is not practical, since the system becomes unstable
due to inaccuracies in inverters output frequency, which leads to increasing circulating
currents.
3.4 : Adaptive Droop Control
29
3.4 Adaptive Droop Control
In this section, based on the estimation of the grid parameters provided by the identification algorithm, an adaptive droop controller able to inject active and reactive power
into the grid with high accuracy is proposed.
3.4.1 Power flow analysis
Using (3.5) and (3.6), as they depend highly on the grid impedance (Zg ∠θg ) is possible
to transform P and Q into novel variables (Pc and Qc ) which are independent from the
magnitude and phase of the grid impedance
Pc = (P sin θg − Q cos θg ) ,
(3.11)
Qc = (P cos θg − Q sin θg ) .
(3.12)
By substituting 3.5 and 3.6 into 3.11 and 3.12, it yields the following expressions
Pc = (EVg sin φ) ,
(3.13)
2
Qc = EVg cos φ − Vg .
(3.14)
Note that Pc is mainly dependent on the phase, while Qc depends on the voltage
difference between the VSI and the grid (E − Vg ). Once these control variables (Pc and
Qc ) are obtained, we can use them into the droop control method to inject active and
reactive power.
Similarly, with the aim to inject the desired active and reactive powers (defined as
P and Q∗ ), the following droop control method which uses the transformation (3.11)
∗
and (3.12), is proposed
φ = −Gq (s)Zg [(P − P ∗ ) sin θg − (Q − Q∗ ) cos θg ] ,
(3.15)
E = E ∗ − Gq (s)Zg [(P − P ∗ ) cos θg + (Q − Q∗ ) sin θg ] ,
(3.16)
Chapter 3 : Adaptive Droop Method
30
Q*
−
Q +
Qc
Gq ( s )
Adaptive
Droop
Controller
+
−
P/Q
Decoupling
Transformation
E*
E
P*
−
P +
Pc
Zg
ω*
θg
Vref *
φ
G p (s)
E sin(ωt − φ )
Droop functions
Figure 3.5: Block diagram of the adaptive droop control.
where E ∗ is the amplitude voltage reference, which takes the values of the estimated
grid voltage (Vg ). By using these equations we can obtain the voltage reference of the
∗
VSI: Vref
= E · sin(ω ∗ t + φ), being ω the angular frequency of the output voltage. The
compensator transfer functions of Pc and Qc can be expressed as
mi + mp s + md s2
,
s
ni + np s
Gq (s) =
.
s
Gp (s) =
(3.17)
(3.18)
In practice, the derivative term in Gq (s) is avoided since it barely affects the system
dynamics. Figure 3.4 shows the block diagram of the droop controller proposed to
inject the desired active P ∗ and reactive power Q∗ .
3.4.2 Small signal modeling
In order to show the system stability and the transient response, a small signal analysis
is provided allowing the designer to adjust the control parameters [21, 36]. Taking into
account that P and Q are the average values of the instantaneous active and reactive
3.4 : Adaptive Droop Control
31
power p(t) and q(t), it can be expressed as
Z
1 t−T
P = vd id =
p(t)dt,
T t
Z
1 t−T
Q = vq id − vd iq =
q(t)dt,
T t
(3.19)
(3.20)
being T the period of the grid frequency. By using the first order Padé approximation,
the average value P and Q can be stated
e−T s ≈
2 − Ts
.
2 + Ts
(3.21)
By substituting (3.13), (3.14) and (3.15), (3.16) into (3.19) and (3.20), and using a small
signal approximation to linearize the equations, it yields
1
· (Vg sin Φê(s) + Vg E cos Φφ̂(s)),
1 + (T /2)s
1
Q̂c =
· (Vg cos Φê(s) − Vg E sin Φφ̂(s)),
1 + (T /2)s
P̂c =
(3.22)
(3.23)
where the lower-case variables with the symbolˆindicate small signal values, and uppercase variables are the steady-state values. By using (3.15), (3.16), (3.17), (3.18) and
(3.22), (3.23) it can be obtained
mi + mp s + md s2
φ̂(s) =
p̂c (s),
s
ni + np s
ê(s) = −
q̂c (s).
s
(3.24)
(3.25)
From (3.24), (3.25) it can be derived the following expressions
mi + mp s + md s2
Vg sin Φê(s) + Vg E cos Φφ̂(s)
φ̂(s) = −
·
,
s
1 + (T /2)s
ni + np s
Vg cos Φê(s) − Vg E sin Φφ̂(s)
ê(s) = −
·
.
s
1 + (T /2)s
(3.26)
(3.27)
By combining (3.26) and (3.27), a fourth order characteristic equation can be obtained
a4 s4 + a3 s3 + a2 s2 + a1 s + a0 = 0.
(3.28)
Chapter 3 : Adaptive Droop Method
32
being,
a4 = T 2 + 2T md Vg E cos Φ,
a3 = 4T + 4md np Vg2 E + 2Vg cos Φ(2md E + T np + T mp E),
a2 = 2Vg cos Φ(T mi E + T ni + 2np + 2mp ) + 4Vg2 E(mp np + md ni ) + 4,
a1 = 4Vg cos Φ(ni + mi E) + 4Vg2 E(mi np + mp ni ),
a0 = 4ni mi EVg2 ,
where the steady-state values of the active and reactive power are P = P ∗ and Q = Q∗ ,
and, from (3.5) and (3.6), the steady-state phase and amplitudes can be calculated as
follows
P ∗ sin θg − Q∗ cos θg
Φ = arctan
P ∗ cos θg + Q∗ sin θg + (Vg2 /Zg )
Vg2 cos θg + P ∗Zg
E=
.
Vg (cos θg cos Φ + sin θg sin Φ)
,
(3.29)
(3.30)
By using this model, it is possible to determinate the system stability by extracting the
root locus family that can be seen in Figures 3.6, 3.7, and 3.8, by changing mp , md , and
nd . In order to guarantee the stability condition (input/output behavior) of the closedloop system dynamics, a poles study of the fourth order identified model is employed.
The performance of this ind of system is often viewed in terms of pole dominance. The
a0 coefficient of the characteristic equation depends basically of mi and ni parameters
that influence directly over the system fast response making it more damped. In some
practical cases it is possible to adjust these parameters for fine-tuning purposes. Moreover, system stability can be determined by using (3.29) when islanding mode is taking
place. In an autonomous operation mode, system stability can be compromised if any
reactive power contributions from the main grid are considered. It is possible to solve
if the parameter ni in (3.29) equals to 0, reducing the system dynamics to a third order
equation. That is why the fourth order system can be simplified to a third, second, or
even first-order system.
3.5 : Control Structure
33
Figure 3.6: Trace of root locus for 0.00005 < mp < 0.0001.
Root Locus
30
20
λ3
Imaginary Axis
10
λ1
λ2
0
-10
λ4
-20
-30
-100
-80
-60
-40
-20
0
Real Axis
Figure 3.7: Trace of root locus for 1x10−6 < mi < 4x10−5.
3.5 Control Structure
Figure 3.9 shows the proposed block diagram of the whole control structure of the
VSI unit with grid-connected to autonomous mode transition capability. It consists
Chapter 3 : Adaptive Droop Method
34
Root Locus
1
0.8
0.6
Imaginary Axis
0.4
0.2
λ1
λ2
0
λ3
λ4
-0.2
-0.4
-0.6
-0.8
-1
-350
-300
-250
-200
-150
-100
-50
0
Real Axis
Figure 3.8: Trace of root locus for 0.0004 < np < 0.01.
of several control loops, described as follows. The inner control loops regulate the
inverter output-voltage and limit the output current. The loop of the SOGI-FLL and the
associated algorithm is able to estimate the grid parameters: frequency, voltage, and
module and angle of the grid impedance (ωg , Vg , Zg , and θg ). These parameters are
used by the adaptive droop controller to inject the required active and reactive power
by the VSI into the grid. In addition, the estimation of the grid impedance can be useful
for islanding detection. If Zg < 1.75 or Zg changes more than 0.5 in 5s, the VSI will
be in island mode. Islanding detection is necessary in order to achieve soft transition
between grid-connected and islanding mode for a non-planned islanding scenario. In
that case, the integral term of the reactive power control must be disconnected (ni = 0)
[23]. Starting from islanding mode the VSI is supplying the local load. When the grid
is available, the VSI must start the synchronization process with the phase, frequency
and amplitude of the grid, without connecting the bypass switch (indicated by the grid
status variable /GS in Figure 3.10. Phase and frequency synchronization can be done
by multiplying the quadrature component of the voltage grid by the VSI voltage, and
processing this signal through a low pass filter and a PI controller to be sent to the phase
control loop. In order to adjust the voltage amplitude, the rms voltage error between
the grid and the VSI must be calculated, and process it through a PI to be sent to the
3.6 : Simulation Results
In verter
L
Local
load
35
B yp a ss
Vg
Zg
C
Grid
VSI
v pcc
i pcc
Driver and
PWM
generator
Current
Loop
Voltage and
current
Monitoring
SOGI-FLL
Voltage
Loop
Inner loops
Transformation
Sine
generator
Vref
Grid parameters
Ident. Algorithm
(Estimated Values)
d −q
E sin(ω ⋅ t − φ )
φ
ωg
Vg
Zg
θg
ω* E*
Droop
E control
PC
P/Q Decoupling
QC Transformation
(Eq. 8)
−
+
+
−
P
*
P
Q
Q
*
Figure 3.9: Block diagram of the SOGI and the proposed adaptive
droop control strategy.
amplitude control loop. Hence, after several line-cycles the VSI will be synchronized
to the grid and the bypass can interconnect the VSI and the grid. At this moment, the
desired active and reactive powers can be injected to the grid.
3.6 Simulation Results
The proposed control is tested through proper simulations in order to validate its feasibility. A single-phase VSI with the controller proposed was simulated by using the
control and system parameters shown in Table 3.1.
Figure 3.11 illustrates the grid impedance estimator performance. The inductive part
of the grid impedance changes from 1.50mH to 1.65mH at t = 10s, while the resistive
part changes from 1.1 to 1 at t = 14s. As can be observed, the transient values cannot
be sent directly to the droop-controller of the VSI. For that reason, a small mismatch is
appreciated due to the buffer of the grid parameters estimation algorithm (see Section
3.1).
Figure 3.12 demonstrates the validity of the model, showing a good resemblance
Chapter 3 : Adaptive Droop Method
36
Power Calculation
Zg
θg
QC
Q+
ipcc
−
LPF
Q* = 0
+90º
v pcc
ipcc
PC
P
LPF
VG
PI (s)
GS
Phase Synchronization
+
+
E * ES
GS
P+
−
Gp (s)
*
φS
+
(Freezing)
P/Q
Decoupling
LPF
−
Gq (s)
+
VG ( rms ) −
LPF
E
φ
−
+
Vref*
E sin(ω ⋅ t − φ )
φS
PI (s)
VC ( rms )
GS
Amplitude Synchronization
Figure 3.10: Block diagram of the whole proposed controller using
the synchronization control loops.
Table 3.1: System Parameters
P arameter
Symbol
Voltage Grid
Vg
Frequency Grid
ω
Resistive Part of Zg
Rg
Inductive Part of Zg
Zg
Grid Z module
Lg
Grid Z angle
θg
Integral phase droop
mi
Proportional phase droop
mp
Derivative phase droop
md
Proportional amplitude droop
np
Integral amplitude droop
ni
V alue
Units
311
V
50
Rad/s
2
Ω
3
mH
2.3
Ω
28.8
Ws/rd
0.0018
W/rd
0.00004 W/rd·s
7e-7
VAr·s/V
0.15
VAr/V
0.0004
VAr/V
ES
R [ Ohm s]
3.6 : Simulation Results
1. 1
1
R
R es t
0. 9
0. 8
1. 7
L [ H]
37
8
x 10
10
12
14
16
18
1. 6
L
L e st
1. 5
1. 4
20
-3
8
10
12
14
16
18
20
Figure 3.11: Variations of the grid impedance, R and L estimation.
between the system phase dynamics and the obtained model (3.29). The model has been
proven for a wide range of grid impedance values, showing its validity. In addition, to
illustrate the robustness in front of large grid impedance variations, some simulations
have been performed with and without the estimator algorithm. Figure 3.13 shows the
transient response of the active power by using the control with and without the grid
impedance estimation loop, for grid impedance variations (Rg = 1, 2, and 3). Notice
that this loop decouples to a large extent the system dynamics from the grid impedance
value.
Figure 3.14(a) shows the synchronization process of the output voltage inverter respect to the grid voltage, during islanding operation. Figure 3.14(b) depicts the voltage
difference between the voltage grid and VSI voltages. Once the synchronization is done,
Figure 3.14(c) shows the transition from islanded mode to grid-connected mode. When
the connection is realized and the system is under a steady-state condition, the active
and reactive power injected to the grid can be independently controlled. Finally, the
system is intentionally disconnected (t = 20s) in order to validate the transition operation from grid-connected to island mode. The seamless transfer can be seen between
both modes, pointing out the flexible operation of the VSI.
Chapter 3 : Adaptive Droop Method
38
10
x 10
-3
8
Phase [rd]
6
4
2
M odel
Real
0
-2
0
0.2
0.4
0.6
0.8
1
Tim e [s]
Figure 3.12: Transient response of the system dynamics and the
obtained model (18).
3.7 Experimental Results
Experimental results have been obtained in order to show the feasibility of the controller proposed. The hardware setup shown in Figure 3.15 consists of the following
equipment: a Danfoss VLT 5006 7.6kVA inverter with and LC filter (L=2x712µH and
C=2.2µF ), and a local load. A dSPACE 1104 system is used to implement the controller. The system sampling and switching frequency were running at 8kHz.
The inverter is connected through a bypass switch to a 5kVA low-voltage grid transformer with an equivalent impedance of 10 mH. The waveforms presented here were
obtained through the ControlDesk software provided by dSPACE, as shown in Figure
3.16. By using this platform we can adjust in real-time the main control parameters
within the specified limits. It includes the coefficients and references of the inner voltage and current control loops, the synchronization loop, and the active and reactive
power outer control loops. Figure 3.17 shows the synchronization process of the inverter with the grid. As it can be seen, in less than 1s the inverter is synchronized to
the grid. Afterwards, the inverter can be connected to the grid and, at that moment, we
can change the power references, as also shown in Figure 3.17. Figure 3.18 shows the
dynamics of the active power when changing the reference from 0 to 1 kW, from 0 to
3.7 : Experimental Results
39
1600
1400
1200
1000
800
600
400
200
R=1
R=2
R=3
0
-200
0
0.5
1
1.5
2
a)
1600
1400
1200
1000
800
600
400
200
R=1
R=2
R=3
0
-200
0
0.5
1
1.5
2
b)
Figure 3.13: Start up of P for different line impedances, (a) without
and (b) with the estimation algorithm of Zg .
500 W, and Figure 3.19 a power step change from 500 W to 1000 W while keeping
Q = 0 VAr. Figure 3.20 shows the capability of the VSI to absorb 1000VAr of reactive power. Notice the transient response and steady-state performances that endows
the controller to the system. Figure 3.21 depicts the transition from islanded mode to
grid-connected mode after the synchronization process (grid and VSI voltages), and
P,Q step changes. Note how the active and reactive power injected to the grid can be
independently controlled.
Chapter 3 : Adaptive Droop Method
40
a)
b)
c)
Figure 3.14: Transition from islanding to grid-connected mode:(a)
synchronization process (grid and VSI voltages), (b)
error between grid and inverter voltages, and (c) P and
Q behavior in both operation modes.
Finally, the system is intentionally disconnected (t=11s). Notice the good resemblance between the experimental results and the corresponding simulation results shown
in Figure 3.14(b)
3.7 : Experimental Results
41
Local Bypass Transformer
5kVA
load
PWM inverter L =713µ H
VDC
400V
Z
C = 2.2 µ F
+
−
Grid
L =713µ H
10mH
ic Vc
Vg
ig
dSPACE
Figure 3.15: Scheme of the experimental setup.
Figure 3.16: Panel supervisor of the ControlDesk from the dSPACE.
Chapter 3 : Adaptive Droop Method
42
a)
b)
Figure 3.17: Synchronization of the inverter to the grid: (a) voltage
waveforms (b) error between grid and inverter voltages.
3.8 Conclusions
In this Chapter, a novel control for a VSI able to operate both islanding and grid connected mode has been presented. In this last case, the inverter is able to inject the desired
active and reactive power to the grid. The control has two main structures. The first one
is the grid parameters estimation, which calculates the amplitude and frequency of the
grid, as well as the magnitude and phase of the grid impedance. The second one is a
droop control scheme, which uses these parameters to inject independently active and
reactive power to the grid. The proposed droop control uses such parameters to close the
loop, achieving a tight P and Q regulation. Thanks to the feedback variables of the estimator, the system dynamics are well decoupled from the grid parameters. The results
point out the applicability of the proposed control scheme to DG VSIs for Microgrid
applications.
3.8 : Conclusions
Figure 3.18: Active power transient response for Q = 0 V Ar from 0
to 1000W (P: blue line, Q: black line).
Figure 3.19: Active power step change for Q = 0 V Ar (P: blue line,
Q: black line).
43
Chapter 3 : Adaptive Droop Method
44
a)
b)
Figure 3.20: Reactive power transient response from 0 to -1000VAr
for P= 0W. (P: blue line, Q: black line).
Figure 3.21: Power dynamic during transition from islanding to
grid-connected mode.
C HAPTER 4
D ROOP
CONTROL METHOD APPLIED
FOR VOLTAGE SAG MITIGATION
4.1 Introduction
The IEEE Standard 1547 [1, 2] defines the ancillary services in distributed power generation systems (DPGS) as: load regulation, energy losses, spinning and non-spinning
reserve, voltage regulation, and reactive power supply. It recommends that low-power
systems should be disconnected when the grid voltage is lower than 0.85p.u. or higher
than 1.1 p.u. as an anti-islanding requirement [1, 2]. Among low-power DPGS, the
number of PV plants connected to low-voltage distribution lines has been increased
in recernt years [11, 12]. Hence, the distributed PV systems should be designed to
comply with anti-islanding requirements, but they can also sustain the voltage for local loads. Usually, grid-connected PV inverters work like current sources (CSI), in
which the voltage reference is often taken from the grid voltage sensing using a phaselocked-loop (PLL) circuit, while an inner current loop ensures that the inverter acts as
a current source. However, in order to maintain the voltage and frequency stability,
voltage source inverters (VSI) are convenient since they can provide ride-through capability to the DPGS, island mode operation, power quality enhancement, and Microgrid
functionalities [34]. Several control techniques based on the droop method have been
proposed to connect VSI system in parallel to avoid communications between them.
Droop method can be an useful way to control active and reactive power injected to the
45
46
Chapter 4 : Droop control method applied for voltage sag mitigation
grid. However, in this last case, the droop method has several problems to be solved,
like line impedance dependence, bad regulation of active and reactive powers, and slow
transient response.
This chapter is focused on a single-phase multifunctional inverter for PV systems application improved with additional power quality conditioning functionalities.
The PV grid-connected converter is controlled on the basis of the droop control technique [27, 28, 34] which provides not only the voltage reference for the repetitive controller [61, 62], but it will also provide active power to local loads and injects reactive
power into the grid voltage at fundamental frequency. Hence, it allows voltage sags
compensation capability to be obtained, endowing voltage ride-through to the system.
The proposed system can also support the voltage applied to local loads in the presence
of voltage sags. A model and analysis of the whole system is given to properly choose
the control parameters. Simulation and experimental results validate the proposed control using a 5kVA PV converter.
4.2 Voltage and frequency support
The power transfer between two sections of the line connecting a DPGS converter to the
grid can be derived using the infinite bus model and complex phasors. From Figure 4.2,
is possible to deduce that Zg = R + jX = Zg · e−jθg = Zg (cos θg + j sin θg ), being Zg
as the line impedance. The analysis below is valid for both single-phase and balanced
three-phase systems. According to Figure 4.1, when the DPGS inverter is connected
to the grid through a generic impedance, the active and reactive powers injected to the
grid can be expressed as follows:
1 EVg cos φ − Vg2 cos θg + EVg sin φ cos θg ,
Zg
1 Q=
EVg cos φ − Vg2 sin θg − EVg sin φ cos θg ,
Zg
P =
(4.1)
(4.2)
where E is the VSI voltage, Vg is the grid voltage, φ is the phase between E and Vg .
Considering that θg ≈ 90◦ , Zg ≈ X the line impedance is mainly inductive X ≫ R, R
may be neglected. Consequently, (4.1) and (4.2) can be rewritten as:
4.2 : Voltage and frequency support
47
P, Q
VSI
E ∠φ
Z g ∠θ g = Rg + jX L
Vg ∠0º
Figure 4.1: Scheme of the power flow transfer through the utility
grid.
Zg
Z g sin θ g
θg
Z g cos θ g
Figure 4.2: Graphical representation of the line impedance vectors.
EVg
sin φ,
X
EVg cos φ − Vg2
Q=
.
X
P =
(4.3)
(4.4)
Arranging (4.3) and (4.4) and considering that the power angle φ is small,then
sin φ ∼
= φ and cos φ ∼
= 1, the phase and the voltage difference between the grid and
the VSI can be calculated as:
X
P,
EVg
X
E − Vg ≈ Q.
Vg
φ≈
(4.5)
(4.6)
Chapter 4 : Droop control method applied for voltage sag mitigation
48
From these equations, it is possible to deduce that the power angle depends predominantly on the active power, whereas the voltage difference E − Vg depends predominantly on the reactive power. In other words, the angle φ can be controlled by regulating the active power, whereas the inverter voltage E is controllable through the reactive
power. The frequency control dynamically controls the power angle and, hence, the real
power flow. Thus, by adjusting the active power P and the reactive power Q independently, frequency and amplitude of the grid voltage are determined. These conclusions
form the basis of the frequency and voltage droop control through respectively active
and reactive power.
4.3 Multifunctional converter for voltage sags mitigation
A. Shunt-converter for Voltage Sags mitigation
Often, series-converter topologies using instantaneous power theory are applied
to multifunctional inverters with ride-through capability in presence of grid voltage
sags [75], [52]. Alternatively, shunt devices are usually adopted to compensate small
voltage variations which can be controlled by reactive power injection. Examples of applications can be found in line interactive uninterruptible power systems or active power
filter topologies [4–6, 31, 44, 65, 79]. The ability to control the fundamental voltage at
a certain point depends on the grid impedance and the power factor of the load. The
compensation of voltage sags by current injection is difficult to achieve, because the
grid impedance is usually low and the injected current has to be very high to increase
the load voltage. The shunt converter can be current or voltage controlled for voltage
sag compensation as shown in Figure 4.3. Following these figs, it is possible to observe
that
−
→ −
→ −
→
Ic = Ic + IL ,
(4.7)
where IC , IG and IL are the currents delivered from the converter, to the grid, and to the
load, respectively. Figure 4.4(a) shows the vector diagram of the voltage and currents.
4.3 : Multifunctional converter for voltage sags mitigation
IG
LG
+
V
IC
−
IL
49
IL
IG
+
+
RL
−
E
LG
V
+
RL
E
−
−
(b)
(a)
Figure 4.3: Equivalent circuit of the power stage of shunt converters:
(a) Current controlled. and (b) Voltage controlled.
IC '
I Gd
I Gq
E
IL '
E
IC
IC
IL
φ
φ
V ∠0º
IG
V ' ∠0º
I Gq
(a)
(b)
Figure 4.4: Vector diagram of the shunt converter providing both
active and reactive power: (a) normal conditions; (b)
voltage sag compensation of 0.15p.u.
Note that when the amplitudes E and Vg are equal, only active power (direct IG )
flows into the inductor LG . Therefore, if the controller is designed to provide only
reactive power, when a voltage sag occurs Vg′ < E, and
−
→′
−→
Ic = IGd + j IGq ,
(4.8)
−→
with IGd = IG , and IGq is the reactive current needed to compensate the voltage sag.
The amplitude of the grid current depends on the value of the grid impedance since
−
→
Ic =
E∠φ−Vg ∠0o
,
jX
(4.9)
where X is the inductor reactance (ωLG ). If the shunt controller supplies the load with
Chapter 4 : Droop control method applied for voltage sag mitigation
50
both active and reactive power, in normal conditions it provides a compensating current
−
→
−
→
−
→
IC = IL , hence, the system operates as in island mode and IG = 0. In the case of a
voltage sag, the converter has to provide the active power required by the load and must
still inject the reactive power needed to stabilize the load voltage as shown in Figure
4.4(b). The grid current in this case is mainly reactive.
It can be observed that during a voltage sag, the amount of reactive current needed
to maintain the load voltage at the desired value is inversely proportional to the grid
impedance. This means that a large inductance will help in mitigating voltage sags.
4.4 Power stage configuration
In case of P V systems, it can be advantageous to use the shunt-connected P V converter also for the compensation of small voltage sags. In this hypothesis, it is possible
to control the voltage directly in order to stabilize the voltage profile while the current
injection is controlled indirectly. Hence, the converter acts as a voltage source, supplying the load and maintaining the load voltage constant. Usually, the impedance of
low-voltage distribution lines is mainly resistive, but, in the proposed topology, the P V
converter is parallel connected to the grid through an extra inductance LG (as shown in
Figure 4.3).
From the exact expression of (4.3), we can conclude that the maximum active power
transferred from or to the grid limits the maximum value of the inductance, as follows
X<
EVg
,
Pmax
(4.10)
whereas Pmax is the maximum active power delivered by the VSI (θg = 90◦ ). By adding
this inductance (LG ), the grid can be considered mainly inductive. In this hypothesis, it
is possible to control the frequency and the voltage amplitude by adjusting active and
reactive power independently. However, it is not convenient to choose a high value inductance LG since the voltage regulation is directly affected by its voltage drop. The
P V system shown in Figure 4.5 is controlled in order to provide the active and reactive
power required. The converter is controlled with three control loops: in the outer one,
4.4 : Power stage configuration
ω LG
Vg ∠0º
51
PG , QG
PL , QL
PC , QC
IG
IL
Load
IC
VC
Inner
loop
VC
IG
Q
calculation
QG
Q* = 0
−
Repetitive
Control
+
Vref
Droop
Control
PC
+
−
I ref
PI
control
Outer P/Q control loop
VC
P
P* calculation
IC
( MPPT )
Figure 4.5: Block-diagram of the grid-connected PV system power
stage and its control scheme.
the droop controller provides the voltage reference for the repetitive controller. It is
possible to modify this voltage reference with the addition of another control loop designed to eliminate the average current present in the system due to a small offset in the
inverter output voltage. This offset can be generated by errors in the voltage and current
sensors, and by the physical differences between the upper and lower switches of the
legs in the PWM inverter bridge [75], [52]. The new reference voltage is denoted in Figure 4.5 as Vref . Hence, the voltage error is pre-processed by the repetitive controller,
which is the periodic signal generator of the fundamental component of the selected
harmonics. This kind of controller is suitable in cases where nonlinear loads are used,
since it is able to supply current harmonics while maintaining low voltage distortion
THD. In this case the third and the fifth ones are compensated [61], [62]. Finally the PI
controller, in the inner loop, improves the stability of the system offering low-pass filter
function. In the presence of a voltage sag, the grid current IG is forced by the controller
to have a sinusoidal waveform which is phase shifted by almost 90◦ with respect to the
corresponding grid voltage.
52
Chapter 4 : Droop control method applied for voltage sag mitigation
E
Vg > E
E = Vg
Vg < E
Q
Q<0
Q>0
Figure 4.6: Relationship between the droop-based controller.
Vg ∠0º
QG
LG
+
E
RL
Figure 4.7: Power flow circuit in presence of a voltage dip.
4.5 Control design
The aim of this section is to develop a control structure for the proposed PV shuntconnected converter. The control objectives of the droop-based controller can be
summed up as follows:
⊲ Enhances the stability and the dynamic response by damping the system.
⊲ Provides all the active power given by the PV source, and extracted in the previous
stage by the maximum power point tracker (MPPT) [64].
⊲ Supports the reactive power required by the grid when voltage sag is presented
into the grid [75].
4.5 : Control design
53
PG , QG
+
LG
PL , QL
+
E RL
Vg
PC , QC
a)
IG
Vg ∠0º
LG
RG
RL
b)
Figure 4.8: Power flow-based circuit modeling. a) Equivalent circuit
b) General approach.
These three control objectives can be achieved by using the following control loops; the
first one is done by implementing a virtual resistor, via the VSI control [34]:
∗
Vref < Vref
− IG · RG .
(4.11)
However, adding damping into the system implies that the impedance seen by the VSI is
not pure inductive, i.e. Rg + jLG . Figure 4.5 depicts the block diagram of this proposed
control strategy in which Vc and Ic denote the converter voltage and current, and Ig the
grid current. By multiplying Vc by Ic and filtering the result, it is possible to obtain the
active power delivered by the converter (Pc ). On the other hand, multiplying Vc delayed
90o by Ig , and then filtering the resulting value it, the reactive power flow from/to the
grid (Qg ) can be obtained
1 EVg − Vg2 cos θg + EVg φ sin θg ,
Zg
1 QC ,
EVg − Vg2 sin θg − EVg φ cos θg ,
Zg
PC ,
(4.12)
(4.13)
54
Chapter 4 : Droop control method applied for voltage sag mitigation
being tan θg = X/R. Based on the information of Figure 4.9, it is possible to calculate
both the active P and reactive Q powers injected to the grid by the VSI, as can be seen
in (4.1) and (4.2) For possible simplifications, is possible to transform P and Q to novel
variables defined as P ′ and Q′ , which are independent from the magnitude and phase of
the grid impedance:
P′ ∼
= PC sin θg − QG cos θg ,
(4.14)
Q′ ∼
= PC cos θg + QG sin θg .
(4.15)
By substituting (4.12), (4.13) into (4.14), (4.15) the following expressions are yielded:
EVg
sin φ,
Zg
EVg
Q′ =
cos φ − Vg2 .
Zg
P′ =
(4.16)
(4.17)
Note that P ′ is mainly dependent on the phase φ, while Q′ depends on the voltage
difference between the VSI and the grid (E − Vg ), as in pure inductive case (4.5), (4.6).
These new control variables (P ′ and Q′ ) are independent from the grid impedance
angle θg , thus we can use them into the droop method to control the active and reactive
power flows. In order to inject the desired active power (Pc′ , which should coincide
with the power given by the MPPT), and to compensate the reactive power (normally
Q′c = 0), the following droop method control loops which uses the transformation
(4.16),(4.17) are proposed
φ = −Gp (s) [(PC − PC∗ ) sin θg − (QG − Q∗G ) cos θg ] ,
(4.18)
E = E ∗ − Gq (s) [(PC − PC∗ ) cos θg + (QG − Q∗G ) sin θg ] .
(4.19)
A PI controller is proposed to ensure that the VSI injects the active power delivered
by the MPPT stage. On the other hand, a proportional controller is proposed for the
reactive power compensation defined as Gp (s) and Gq (s), respectively:
mi + mp s
,
s
Gq (s) = np .
Gp (s) =
(4.20)
(4.21)
4.6 : System dynamics and control parameters design
LPF
+90º
−
Gq (s)
−
QG* = 0
+
V*
P/Q
Decoupling
VC
IC
Q'
QG +
IG
55
LPF
Power Calculation
V
P'
PC +
Gp (s)
−
PC *
φ
−
+
Vref* + Vref
V sin(ωt − φ )
−
φ*
LPF
Figure 4.9: Block diagram of the droop control loops.
For reactive power compensation support, the coefficient np must be properly adjusted.
By using (4.4), (4.6), (4.19) and (4.21) with θg = 90o and Vg = αE ∗ (being α as the
voltage sag percentage), is possible to obtain:
np =
E ∗ α(1 − α) − Qmax X
,
Qmin E ∗ α
(4.22)
where Qmax is the maximum reactive power flow that can be delivered by the VSI.
Figure 4.9 shows details of the block diagram implementation of the droop controller,
which is able to inject the desired active power Pc∗ and to compensate reactive power
Qg .
4.6 System dynamics and control parameters design
In this section, the system dynamic model and the stability analysis are provided to
properly design mi and mp coefficients of the PI compensator (4.20), corresponding to
the active power injection control loop (4.18). A small signal analysis is provided in
order to show the system stability and the transient response. The power calculation
block uses a low pass second order filter in which the pass band is much smaller than
the pass band of the inverter voltage control. Hence, both the power and reactive output
Chapter 4 : Droop control method applied for voltage sag mitigation
56
power measured from the power calculation block can be defined as:
ωo2
p̂′ (s),
s2 + 2ζωos + ωo2
ωo2
q̂meas (s) = 2
q̂ ′ (s),
s + 2ζωos + ωo2
p̂meas (s) =
(4.23)
(4.24)
where ωo is the resonance frequency, and ζ the damped coefficient. By doing a small
signal approximation in order to linearize the equations, it yields
"
#
Vg sin Φê(s) + Vg E cos Φφ̂(s)
ωo2
p̂meas (s) = 2
,
s + 2ζωos + ωo2
Zg
"
#
ωo2
Vg cos Φê(s) − Vg E sin Φφ̂(s)
q̂meas (s) = 2
+ ωo2 q̂ ′ (s),
s + 2ζωos + ωo2
Zg
(4.25)
(4.26)
where the lower-case variables with the symbolˆindicate small signal values, and uppercase variables are the steady-state values. By using (4.20), (4.21) and (4.24), (4.25)
we can obtain
mi + mp s
p̂meas (s),
s
ê(s) = −ni q̂meas (s).
φ̂(s) = −
(4.27)
(4.28)
From (4.27), (4.28) the following expressions can be derived
mi + mp s Vg sin Φê(s) + Vg E cos Φφ̂(s) ,
s
ê(s) = −ni Vg cos Φê(s) − Vg E sin Φφ̂(s) .
φ̂(s) = −
(4.29)
(4.30)
By combining (4.25), (4.26) and (4.27), we can be obtain the following fifth order
characteristic equation
s5 + a4 s4 + a3 s3 + a2 s2 + a1 s + a0 = 0
(4.31)
4.6 : System dynamics and control parameters design
57
Being,
a4 = 4ωo ζZg ,
(4.32)
a3 = Vg ωo2 cos Φ(np + Emp ) + 2ωo2(1 + 2ζ 2)Zg ,
(4.33)
a2 = 2Vg ωo2 ζ cos Φ(np + Emp ) + ωo2 Vg E cos Φmi + 4ζωo3Zg ,
Vg
a1 = Vg ωo4 cos Φ(np + Emp ) + Vg Eωo3(2ζ cos Φmi + ωo np mp ) + ωo4 Zg ,
Zg
Vg
a0 = Vg Eωo4 mi (cos Φ + np ).
Zg
(4.34)
(4.35)
(4.36)
the steady-state values of the active power are P = P ∗ , and calculating Q using (4.2)
in steady-state, defined as
Qss =
1 (EVg cos Φ − Vg2 ) sin θg − EVg sin Φ cos θg ,
Zg
(4.37)
the steady-state phase and amplitudes can be calculated from (4.12), and (4.13) as follows
Φ = arctan
E=
Pc′ sin θg − Qss cos θg − EVg sin Φ cos θg
PC′ cos θg + Qss sin θg + (Vg2 /Zg )
Vg2 cos θg + PC∗ Zg
.
Vg (cos θg cos Φ + sin θg sin Φ)
,
(4.38)
(4.39)
The model obtained has been used to extract the family of root locus as can be depicted
in Figure 4.10(a) and Figure 4.10(b). Figure 4.10(a) shows for convenience the dominant poles (λ1 and λ2 ) root locus. It illustrates that when mp is increased, the poles
go toward the imaginary axis, becoming a faster oscillatory system. Fig 4.10(b) depicts
the root locus behavior when mi is increased. Note that λ3 , λ4 , and λ5 are far away
from λ1 and λ2 . Thus, using mp and mi it is possible to locate the poles where it is
more convenient. Furthermore, this dominance can illustrate that the obtained model
can be adjusted as a second or even a first order system. By using this model (4.31), the
stability of the system has been studied for large grid inductance LG variations. Figure
4.10(c) shows that the fifth order system is stable if the value of LG is more than 8mH.
Below this value, the real part of the eigenvalues λ4 and λ5 is positive, so the system
remains unstable. On the contrary, if we increase the value of LG , those eigenvalues are
58
Chapter 4 : Droop control method applied for voltage sag mitigation
a)
b)
c)
Figure 4.10: a) Root locus for 0.00002 < mp < 0.001 and
mi = 0.0002. b) Root locus for
0.000002 < mi < 0.0018 and mp = 0.00006. c) Root
locus diagram for grid inductance variations:
8.5mH < LG < 5000mH.
stable. Although λ2 and λ3 are attracted towards the imaginary axis, they never cross it.
4.7 : Simulation Results
59
Table 4.1: Power Stage and Control Parameters
P arameter
Symbol
Grid voltage
E
Grid frequency
ω
Grid inductance
LG
Load Resistance
R
Sample frequency
Fs
Integral droop P coefficient
mi
Proportional droop P coefficient
mp
Proportional amplitude droop
np
Resonance frequency of measuring filter
ωo
V alue Units
311
V
2π50
Rad/s
15
mH
40
Ω
6400
Hz
0.00002 W/rd
0.006 W/rd·s
0.15
VAr/V
31.4
Rad/s
4.7 Simulation Results
Considering the P V system represented in Figure 4.5, different tests have been performed in order to validate the proposed control. All the physical parameters of the
system are defined in Table 4.1. Figure 4.11 shows the steady-state current waveforms
of the converter, grid,and load (Ic , Ig and IL ). In the case of a purely resistive load
absorbing 1200W , the block diagram shown in Figure 4.9 is modified taking into account that the active power reference Pc∗ should coincide with the nominal active power
and the reactive power reference Q∗c = 0. The results are shown in Figure 4.12. This
figure illustrates the transient response of the active and reactive powers when the active power reference was changed from 1200W to 600W at t = 5s and the reactive
power reference from 0 to 500 V Ar at t = 10s. The results show the P and Q injection
decoupling of the proposed control strategy. The validity of the proposed control has
also been tested in the presence of a voltage sag, equals to 0.15 p.u. which occurs at
t=1.5s (see Figure 4.13). In this case, the converter provides the reactive power needed
to compensate the sag. The current waveforms of the converter, the grid, and the load
are shown in Figure 4.14. A detail of the grid voltage and grid current waveforms during the voltage sag is shown in Figure 4.15 Notice that the controller endows voltage
ride-through capability to the system when voltage sags are presented in the grid.
60
Chapter 4 : Droop control method applied for voltage sag mitigation
Figure 4.11: Steady-state operation during grid normal condition: (a)
Inverter current IC (b) Grid current IG , and (c) Load
current IL .
Similar ride-through capability tests were performed when the active power provided by the inverter (500 W ) is lower than the power required by the load. In this
situation, the grid injects the rest of the power to the system (700 W ), and the system
injects to the grid the necessary reactive power in case of a voltage sag. Figure 4.16
shows the active and reactive power provided by the inverter for a voltage sag, and
Figure 4.17 shows the corresponding current waveforms. From these results, we can
conclude that the system also has ride-through capabilities.
Another test was performed in the case of existence of high-value voltage harmonics
in the grid, as depicted in Figure 4.18. Figure 4.19 shows the voltage current waveforms.
Note that the system injects harmonic current to the grid in order to maintain the quality
of the load voltage waveform Figure 4.18 shows the active and reactive power transient
responses for changes in the power references, as done in Figure 4.12. In this case, the
system also exhibits good tracking performance.
4.7 : Simulation Results
Figure 4.12: Active and reactive power transient responses and step
changes provided by the PV inverter during normal
operation.
Figure 4.13: Active and reactive power provided by the PV inverter
in the presence of a voltage sag of 0.15 p.u.
61
62
Chapter 4 : Droop control method applied for voltage sag mitigation
Figure 4.14: Current waveforms in case of a voltage sag of 0.15p.u.
(inverter current IC , grid current IG , and load current
IL ).
Figure 4.15: Detail of the waveforms during the sag: grid voltage
(upper) [100V/div], and grid current (lower) [10A/div].
Finally, the system was tested by supplying a nonlinear load consisting of a dioderectifier with an RC load, as is depicted in Figure 4.20. Figure 4.21 shows the inverter
output voltage, and the active and reactive power provided. This case exhibits the good
tracking performance, similar to the case of supplying linear loads (see Figure 4.18).
4.7 : Simulation Results
63
Figure 4.16: Active and reactive power provided by the PV inverter
in presence of a voltage sag of 0.15p.u. when
Pc∗ = 500W .
Figure 4.17: Current waveforms in case of a voltage sag of 0.15 p.u.
(inverter current IC (upper), load current IL (middle)
and grid current IG (bottom) when Pc∗ = 500W ).
Figure 4.22 shows the current waveforms of the inverter,the nonlinear load, and
the grid. The system provides shunt active power capabilities, since the grid current
64
Chapter 4 : Droop control method applied for voltage sag mitigation
Figure 4.18: Grid voltage waveform in presence of 1st, 3rd, 5th 7th
and 9th voltage harmonics.
Figure 4.19: Active and reactive power transient responses and step
changes provided by the PV inverter using the distorted
grid waveform.
4.7 : Simulation Results
65
LG
AC power
source
R=40Ω
C=3500µF
C
R
Grid converter
VSI + LC filter
Figure 4.20: Single-phase rectifier with R-C circuit as nonlinear
load.
Figure 4.21: Inverter output voltage (detail), active and reactive
power transient responses under a non-linear load.
waveform is harmonic free and the power factor is near one. According to the obtained
results, the system shows high performances like: active and reactive power tracking,
voltage sags ride-through, voltage and current harmonic compensation.
66
Chapter 4 : Droop control method applied for voltage sag mitigation
Figure 4.22: Current waveforms in case of a non-linear load and Vg
with harmonics: inverter current IC (upper), load
current Il (middle), and grid current IG (bottom).
4.8 Experimental results
Experimental tests have been carried out in a laboratory set-up to test the performance
of the PV system with the shunt-connected multifunctional converter. The hardware
setup shown in Figure 4.23 and it consists of the following equipment: a Danfoss VLT
5006 7.6kVA inverter, on which only two legs are used, hence the apparent power is
2/3 of 7.6kVA, two series connected dc voltage sources to simulate PV panels string and
Dspace 1104 system. A Pacific ac power source emulates the main grid. It is set in order
to provide a voltage sag of 0.15 p.u. The PV multifunctional converter is connected to
the grid through an L-C filter whose inductance is 1.4mH, the capacitance is 5µF in
series with a resistance of 1Ω; besides an inductance LG of 15mH has been added to
the grid impedance as explained in the previous Sections. The performances of the
proposed controllers are in accordance with the simulation results. The experimental
results obtained in the same conditions (voltage sag duration equal to 1.5s) are reported
in Figure 4.24. Figure 4.25 and Figure 4.26 show a detail of the voltage waveforms,
4.9 : Conclusions
67
Figure 4.23: Laboratory Setup
the grid voltage, and the injected current during the sag. Notice that PV converter
provides voltage support and maintaining the load voltage constant by injecting 7A of
pure reactive current into the grid during the voltage sag. These results are in accordance
with the simulation tests (see Figs. 4.13 and 4.14).
4.9 Conclusions
In this chapter, future ancillary services in DPGS should contribute to the reinforcement
of the distribution grid and to maintain proper quality of supply. Also, a single-phase
photovoltaic system with power quality conditioner functionality has been presented.
The voltage-controlled PV converter is shunt-connected to the grid and a droop controller provides the voltage reference where a repetitive algorithm controls the voltage
provided by the PV converter. An inductance has been added on the grid side; hence
it can be considered that the PV system is connected to a mainly inductive grid. The
control strategy of the grid frequency and the grid voltage amplitude is based on the
independent adjustment of active and reactive power. The PV converter provides grid
voltage support at fundamental frequency. In case of a voltage sag, the converter has
to provide the active power required by the load and must still inject the reactive power
needed to stabilize the load voltage. Hence, the system shows high performances like:
68
Chapter 4 : Droop control method applied for voltage sag mitigation
Figure 4.24: Experimental results in case of a voltage sag of 0.15
p.u. (voltage controlled inverter with droop control): 1)
grid current [10V/div], 2) load voltage [400 V/div], 3)
grid voltage [400V/div].
active and reactive power tracking, voltage sags ride-through, voltage and current harmonic compensation. The experimental results confirm the validity of the proposed
solution in the presence of small voltage sags.
4.9 : Conclusions
Figure 4.25: Voltage waveforms during the sag [100V/div]: grid
voltage (channel 4, upper), capacitor voltage (channel
3, middle) and load voltage (channel 3, lower).
Figure 4.26: Waveforms of the grid voltage (channel 4, upper)
[100V/div], and the grid current (channel 1, lower)
[10A/div] during the sag.
69
70
Chapter 4 : Droop control method applied for voltage sag mitigation
C HAPTER 5
H IERARCHICAL
FLEXIBLE
CONTROL FOR
M ICROGRIDS
5.1 Introduction
In Microgrids field, the variable nature of some renewable energy systems, such as photovoltaic (PV) or wind energy, relies on natural phenomena, such as sunshine or wind.
Consequently, it is difficult to predict the amount of power that can be obtained through
these prime sources, and the peaks of power demand do not necessarily coincide with
the generation peaks. Hence, storage energy systems are required if we want to supply
the local loads in an uninterruptible power supply (UPS) fashion [3], [49], [18], [20].
Some small and distributed energy storage systems can be used for this purpose, such
as flow batteries, fuel cells, flywheels, superconductor inductors, or compressed air devices.
The DG concept is growing in importance, pointing out that the future utility line
will be formed by distributed energy resources and small grids (minigrids or Microgrids) interconnected between them [31], [32]. In fact, the responsibility of the final
user is to produce and store part of the electrical power of the whole system. Hence,
Microgrid can export or import energy to the utility through the point of common coupling (PCC). Moreover, when there is utility failure, the Microgrid can still work as
71
Chapter 5 : Hierarchical control for flexible Microgrids
72
an autonomous grid. As a consequence, these two classical applications, namely, gridconnected and islanded operations, can be used in the same application. In this sense,
the droop control method is proposed as a good solution to connect, in parallel, several
inverters in an island mode [8, 14, 39, 60]. However, although it has been investigated
and improved, this method by itself is not suitable for the coming flexible Microgrids.
Further, although there are line-interactive UPSs in the market, still, there are no lineinteractive UPS systems able to operate in parallel autonomously, forming a Microgrid [4], [79].
In this chapter, a control scheme for UPSs connected in parallel, forming a Microgrid, is proposed. The Microgrid presented is formed by parallel-connected UPS
inverters. Its difference from the conventional parallel UPS systems [37, 58, 67] is that
the flexible Microgrid can not only import and export energy to the main grid, but can
also operate in grid-connected or in island modes. The presented application is a PV
system with 6-kV A line-interactive UPS units [13]. The typical applications of these
P V -UPS systems are domestic, up to 30kVA. The UPS inverters use a droop control
function in order to avoid critical communication between the modules. The droop
function can manage the output power of each UPS as a function of the battery charge
level. The inverters, compared to the conventional methods, act as voltage sources even
when they are connected to the grid [28], [84]. In this situation, they are able to share
power with the grid, based on its nominal power. Finally, the intelligent static bypass
switch connects or disconnects the Microgrid and sends proper references to the local
UPS controllers by means of low bandwidth communications.
5.2 Microgrid structure and control
A flexible Microgrid has to be able to import/export energy from/to the grid, control
the active and reactive-power flows, and manage the energy storage. Figure 5.1 shows a
Microgrid, including small generators, storage devices, and local critical and noncritical
loads, which can operate both, connected to the grid or autonomously in island mode.
This way, the power sources (PV arrays, small wind turbines, or fuel cells) or storage
devices (flywheels, superconductor inductors, or compressed air systems) use electronic
5.2 : Microgrid structure and control
73
Wind turbine
UPS
PV
panel system
Inverters
PCC
Utility
Grid
Static
transfer switch
(IBS)
Common
ac bus
...
Distributed loads
Micro-grid
Figure 5.1: Typical structure of inverter Microgrid based on
renewable energies.
interfaces between them and the Microgrid. Usually, these interfaces are ac/ac or dc/ac
power electronic converters, also called inverters. Traditionally, inverters have two separate operation modes acting as a current source, if they are connected to the grid, or as
a voltage source, if they work autonomously. In this last case for security reasons and
to avoid islanding operation, the inverters must be disconnected from the grid when a
grid fault occurs. However, if we want to impulse the use of decentralized generation of
electrical power, the DG, and the implantation of the Microgrids, islanding operation
should be accepted if the user is completely disconnected from the grid. In this case,
the Microgrid could operate as an autonomous grid, using the following three control
levels.
⊲ Primary control: The inverters are programmed to act as generators by including
virtual inertias through the droop method, which ensures that the active and the
reactive powers are properly shared between the inverters.
⊲ Secondary control: The primary control achieves power sharing by sacrificing
frequency and amplitude regulation. In order to restore the Microgrid voltage
to nominal values, the supervisor sends proper signals by using low bandwidth
communications. This control also can be used to synchronize the Microgrid with
74
Chapter 5 : Hierarchical control for flexible Microgrids
the main grid before they have to be interconnected, facilitating the transition
from islanded to grid-connected mode.
⊲ Tertiary control: The set points of the Microgrid inverters can be adjusted, in
order to control the power flow, in global (the Microgrid imports/exports energy)
or local terms (hierarchy of spending energy). Normally, the power-flow priority
depends on economic issues. Economic data must be processed and used to make
decisions in the Microgrid.
Figure 5.1 shows the schematic diagram of a Microgrid. In our example, it consists of several PV strings connected to a set of line-interactive UPSs forming a local
ac Microgrid, which can be connected to the utility mains through an intelligent bypass switch (IBS). The IBS is continuously monitoring both of its sides, namely, the
grid main and the Microgrid. If there is a fault in the utility main, the IBS will disconnect the Microgrid from the grid, creating an energetic island. When the main is
restored, all UPS units are advised by the IBS to synchronize with the mains to properly manage the energy reconnection. The Microgrid has two main possible operation
modes: grid-connected and islanded modes. The transitions between both modes and
the connection or disconnection of UPS modules should be made seamlessly (hot-swap
or plug-and-play capabilities) [25, 41, 57, 94]. In this sense, the droop control method
has been proposed for islanding Microgrids [86]. Taking into account the features and
limitations of the droop method, we propose a control structure for a Microgrid which
could operate in both grid-connected and islanded modes. The operation of the inverters is autonomous, contrary to other Microgrid configurations [37] [67] [58] which use
master-slave principles. Only low bandwidth communications are required in order to
control the Microgrid power flow and synchronization with the utility grid.
5.3 Primary Control Strategy
The control of the UPS inverter is based on three control loops [29]: 1) the inner voltage
and current regulation loops; 2) the intermediate virtual impedance loop; and 3) the
outer active and reactive-power-sharing loops. The inner voltage and current regulation
5.3 : Primary Control Strategy
75
loops can be implemented by using a conventional PI multiloop control or generalized
integrators. The virtual output impedance loop is able to fix the output impedance of
the inverter by subtracting a processed portion of the output current io to the voltage
reference of the inverter Vref [30]. The output impedance for each current harmonic
has been programmed by using a discrete Fourier transformation, as follows [33]:
∗
V = Vref − s
h−H
X
LV h · ioh ,
(5.1)
odd
where V ∗ is the voltage reference of the inner control loops, ioh is the h − th harmonic current, and LV h is the impedance associated with each component. The output
impedance of each harmonic can be adjusted to share properly the load currents but
without greatly increasing the voltage total harmonic distortion (THD). Moreover, a
hot-swap operation, i.e., the connection of more UPS modules without causing large
current disturbances, can be achieved by using a soft-start virtual impedance. The soft
start is achieved by programming a high output impedance at the inverter connection to
the Microgrid. After the connection, the output impedance is then reduced slowly to a
nominal value. This operation can be described by
−t
Lv = L∗Df + (L∗Do − L∗Df ) · e Tst ,
(5.2)
where L∗Do and L∗Df are the initial and final values of the output impedance and Tst is
the time constant of the soft-start operation. Once the output impedance is fixed, the
droop method can operate properly. In the droop equations, derivative terms have been
included to improve the transient response of the system [34]
d(P − P ∗ )
,
dt
d(Q − Q∗ )
E = E ∗ − n(Q − Q∗ ) − nd
,
dt
ω = ω ∗ − m(P − P ∗) − md
(5.3)
(5.4)
where md and nd are, respectively, the active and reactive derivative droop coefficients.
Figure 5.4 shows the block diagram of the control loops of one inverter connected to
the Microgrid, including the inner current and voltage loops; the virtual impedance loop
(5.1) with soft start (5.2); and the power-sharing loops (5.3) and (5.4).
Chapter 5 : Hierarchical control for flexible Microgrids
76
Pg , Qg
Pi* , Qi*
*
Pg , Qg
*
−
+
PI (s)
+
+
DG1
DG2
P * , Q*
Figure 5.2: Power flow control between the grid and the Microgrid.
5.4 Secondary Control Structure
The aim of this section is to develop a flexible control that can operate in grid-connected
and islanded operations and to enable the transition between both modes.
A. Grid-Connected Operation In this mode, the Microgrid is connected to the grid
through an IBS. In this case, all UPSs have been programmed with the same droop
function [29], [33], [82], [9], where P ∗ and Q∗ are the desired active and reactive powers. Normally, P ∗ should coincide with the nominal active power of each inverter, and
Q∗ = 0.
ω = ω ∗ − m · (P − P ∗ ),
(5.5)
E = E ∗ − n · (Q − Q∗ ).
(5.6)
However, we have to distinguish between two possibilities: 1) importing energy from
the grid or 2) exporting energy to the grid. In the first scenario, in which the total
load power is not fully supplied by the inverters, the IBS must adjust P . By using low
bandwidth communications to absorb the nominal power from the grid in the PCC. This
is done with small increments and decrements of P . as a function of the measured grid
power, by using a slow P I controller, as follows:
5.5 : Islanded Operation
77
ω
ω*
Battery 100%
charged
ωg
Battery
30% charged
Pmax P
30% Pmax
Figure 5.3: Droop characteristic as function of the battery charge
level.
∗
P =
kp (Pg∗
− Pg ) + k i
Z
(Pg∗ − Pg )dt + Pi∗ ,
(5.7)
where Pg and Pg∗ are the measured and the reference active powers of the grid, respectively, and Pi∗ is the nominal power of the inverter i. This way, the UPSs with a low
battery level can switch to charger mode by using P ∗ < 0. Similarly, we proposed that
reactive-power control law can be defined as
∗
Q =
kp′ (Q∗g
− Qg ) +
ki′
Z
(Q∗g − Qg )dt + Q∗i ,
(5.8)
where Qg and Q∗g are the measured and the reference reactive powers of the grid, respectively, and Q∗i is the nominal reactive power. The second scenario occurs when
the power of the prime movers (e.g. PV panels) is much higher than those required by
the loads and when the batteries are fully charged. In this case, the IBS may enforce
to inject the rest of the power to the grid. Moreover, the IBS has to adjust the power
references.
5.5 Islanded Operation
When the grid is not present, the IBS disconnects the Microgrid from the main grid,
starting the autonomous operation. In such a case, the droop method is enough to
Chapter 5 : Hierarchical control for flexible Microgrids
78
guarantee proper power sharing between the UPSs. However, the power sharing should
take into account the batteries charging level of each module. In this case, the droop
coefficient m can be adjusted to be inversely proportional to the charge level of the
batteries, as shown in Figure 5.3
m=
mmin
,
α
(5.9)
where mmin is the droop coefficient at full charge and α is the level of charge of the
batteries (α = 1 is fully charged and α = 0.01 is empty). The coefficient α is saturated
to prevent m from rising to an infinite value.
5.6 Transitions Between Grid-Connected and Islanded
Operation
When the IBS detects some fault in the grid, it disconnects the Microgrid from the
grid. In this situation, the IBS can readjust the power reference to the nominal values;
however, this action is not mandatory. Instead, the IBS can measure the frequency and
the amplitude of the voltage inside the Microgrid and move the set points (P ∗ and Q∗ )
in order to avoid the corresponding frequency and amplitude deviations of the droop
method. In contrast, when the Microgrid is working in islanded mode and the IBS
detects that the voltage outside of the Microgrid is stable and fault-free, the islanded
mode can resynchronize the Microgrid with the frequency, amplitude, and phase of the
grid in order to reconnect the Microgrid to the grid seamlessly.
5.7 Small-signal Analysis
A small-signal analysis is proposed to investigate the stability and transient response
of the system. In order to ensure stability, a similar analysis as in [21] has been done,
which results in a third-order system.
5.7 : Small-signal Analysis
79
Figure 5.4: Block diagram of the inverter control loops.
5.7.1 Primary Control Analysis
The closed-loop system dynamics is derived by considering the stiff load-bus approximation [9]. The small-signal dynamics of the active and reactive powers, i.e. P̂ and
Q̂, respectively, are obtained by linearizing (5.5) and (3.8) and modeling the low-pass
filters with a first-order approximation, i.e.
P̂
!
Q̂
V ωc
=
X(s + ωc )
!
cos Φ −E sin Φ
sin Φ
E cos Φ
ê
!
φ̂
(5.10)
where ê denotes perturbed values; capital letters mean equilibrium point values; X
is the output impedance at the fundamental frequency; and ωc is the cutoff angular frequency of the low-pass filters, which are fixed over one decade below the line frequency.
For simplicity, the high-frequency impedance values are not considered in this analysis since they have little effect over the system dynamics. Subsequently, by perturbing
Chapter 5 : Hierarchical control for flexible Microgrids
80
Figure 5.5: Configuration setup for simulation results of the
Microgrid.
(5.3) and (5.4) and using (5.10), we obtain
h
i
V ωc
cos Φ · ê − E sin Φφ̂ ,
Rd (s + ωc )
m
h
i
V ωc
φ̂ = −
+ md
sin Φ · ê − E cos Φφ̂ .
s
Rd (s + ωc )
ê = −(n + nd s)
(5.11)
(5.12)
Finally, substituting (5.11) into (5.12), we can find a third-order small-signal dynamics of the closed-loop system
s3 + As2 + Bs + C = 0
(5.13)
where,
ωc
V
A=
2Rd + nV cos Φ + nd ωc V cos Φ + md V E cos Φ + nd ωc
,
X
X
ωc
V
V
B=
ωc + nωc V cos Φ + mV E cos Φ + nd ωc + md ωc V E cos Φ + n
,
X
X
X
ωc
V
C=
mωc V E cos Φ + n
,
Xd
X
5.7 : Small-signal Analysis
81
Figure 5.6: Root locus plot in function of the batteries charge level
(arrows indicate decreasing value from 1 to 0.01).
with Xd = X + nd ωc V cos Φ. Using (5.13), the stability of the closed-loop system
can be evaluated, and the transient response can be adjusted. The eigenvalues of the
system (λ1 , λ2 , and λ3 ) have been studied by using the power stage and control parameters shown in Table 5.1. Figure 5.6 shows the family of root locus, showing stability
for all battery charge conditions (from α=1 to α=0.01).
5.7.2 Secondary Control Analysis
Secondary control has been analyzed and modeled using a similar approach as in the
last section. By using 5.7 and assuming a P/Q decoupling, the active power, given by
one inverter, can be derived as
−mEV ωc (P ∗ − Pi∗ )
Pi =
,
X(s + ωc )
(5.14)
Chapter 5 : Hierarchical control for flexible Microgrids
82
Table 5.1: Control System Parameters
P arameter
Nominal Frequency
Nominal Amplitude
Nominal virtual output impedance
Initial output impedance value
Soft-start time constant
P Proportional term value
P Integral term value
Q Proportional amplitude droop
Q Integral amplitude droop
Symbol
ω∗
E
L∗Df
L∗Do
TST
kp
ki
kp′
ki′
V alue Units
2pi50
rad/s
311
V
800
µH
80
mH
0.1
s
1.8
W/rd·s
0.1
W/rd
30
VAr/V
80
sVAr/V
where Pi is the active power of the inverter i and Pi∗ is the nominal active power. By
combining 5.8 and 5.14 yields the following second-order transfer function:
Pi
m(ki + kp s)EV ωc
=
.
∗
2
Pg
N(Xs + ωc [X + mEV (nkp − 1)]s + NmEV ωc ki )
(5.15)
By studying the eigenvalues of 5.15, a series of root-locus diagrams is shown in Figure 5.8(a) and 5.8(b), illustrating the stability limits which can be useful for adjusting
the transient response of the system. A similar study can be done for reactive-power
secondary control (12).
5.8 Simulation Results
The aim of this section is to test the proposed controller over the Microgrid in order to
show its performance and limitations in different scenarios.
5.8.1 Harmonic-Current Sharing
The first step is to observe the effect of the proposed controller over the harmoniccurrent sharing, which is very important when the system is supplying a nonlinear load.
5.8 : Simulation Results
83
Figure 5.7: Root locus plot for a) kp = 0.8 and 0.1 ≤ ki ≤ 0.8 b)
ki = 0.5 and 0.7 ≤ kp ≤ 0.8.
With this objective, a series of simulations have been performed for a two-UPS paralleled system sharing a common nonlinear load. Figure 5.9(a) shows the steady-state and
the transient responses of the inverters output currents without using the harmonic sharing loop. In consequence, fundamental currents are equal; however, the third, fifth, and
seventh harmonics are unbalanced. As shown in Figure 5.9(b), by using 5.1, with the
harmonic-current sharing loop, fundamental and harmonic current terms are properly
shared. Note that in this case, up to the seventh harmonic has been included. However,
higher harmonics can be added to this control loop, if necessary.
84
Chapter 5 : Hierarchical control for flexible Microgrids
Figure 5.8: Harmonic decomposition extracted by using the (top)
bank of bandpass filters and (bottom) output currents of a
two-UPS system with highly unbalanced power lines,
sharing a nonlinear load (a) without and (b) with the
harmonic-current sharing loop.
5.8.2 Hot-Swap Operation
The second step consisted in testing the hot-swap operation of the UPS by using the
proposed soft-start impedance. Two main scenarios must be considered, namely, the
connection and the disconnection of the UPS in the distributed system. In the first case,
when an additional UPS has to be connected to the common bus, the output voltage of
the inverter must be synchronized with the bus by a phase-locked loop action. After
that, the droop control method begins operating, together with the output impedance
loop. As stated earlier, at first, the output impedance has a high value; later, however, it
goes down to the nominal value in a soft-start fashion, avoiding initial current peaks.
Figure 5.9 shows the circulating current (io1 − io2 ) between two UPSs sharing a
5.8 : Simulation Results
85
nonlinear load, when UPS#2 is connected at t = 0.8s and while UPS#1 remains
connected from the beginning. Figure 5.9(a) shows the transient response of the circulating current without using the soft-start impedance, thus maintaining the L constant
at 800H. Notice that the circulating current is initially higher than the current supplied
by UPS#1 before the UPS#2 connection. Figure 5.9(b) shows the transient response
using the same configuration but adding the soft-start loop 5.2 with the following parameters: TST = 0.1s and L = 80H. Note that, in this case, the circulating current
has been reduced by half. Figure 5.9(c) shows the dynamic behavior of the circulating
current by increasing L to 800H. Observe now that the system becomes slower while
the initial current peak tends to increase.
Figure 5.10 shows a detail of the connection of UPS#2 while UPS#1 is connected
to the load permanently. A four-UPS system sharing a distributed nonlinear load in
order to see the effects of the inverter connection/disconnection has been simulated, and
the results are shown in Figure 5.15. The impedances of the lines connected between
the inverters and the load were intentionally unbalanced. ZL1 = 0.12 + j0.028, ZL2 =
0.24 + j0.046, ZL3 = 0.06 + j0.014, and ZL4 = 0 + j0 (see Figure 9). Figure 10(a)
shows the progressive connection of the four UPSs to the common ac bus, with UPS#1
at t = 0s, UPS#2 at t = 0.8s, UPS#3 at t = 1.6s, and UPS#4 at t = 2.4s. As it can
be seen, the UPS modules are seamlessly connected to the bus, increasing their output
currents gradually. Figure 5.15(b) shows the disconnection of the UPS from the ac
bus. Note that there are no overcurrents. Droop functions for every UPS accommodate
properly the output currents to the amount of load without critical transients.
5.8.3 Microgrid Operation and Transitions
Figure 5.12 shows the active and reactive powers of a two-UPS Microgrid sharing power
with the grid, the transition to islanded operation, and the disconnection of UPS#2.
Figure 5.13 depicts three UPSs connected to the Microgrid and the main grid showing
the transition from grid connected and island operation (t = 4s). Also, observe how
good the active power sharing is carried out when UPS#1 and UPS#2 are disconnected
(t = 6s and t = 9s respectively). The power sharing is automatically distributed among
the connected inverters corresponding to the slopes of their droops. These results are
86
Chapter 5 : Hierarchical control for flexible Microgrids
(a)
(b)
(c)
Figure 5.9: Circulating current when a second UPS is connected at
t = 0.8 (a) without the soft start, (b) with the soft start
LDo =80 µH, and (c) LDo = 800 µH (Y -axis:2A/div).
5.9 : Experimental Results
87
Zo (H)
0.1
0.05
0
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.8
1
1.2
1.4
1.6
1.8
2
0.8
1
1.2
1.4
time (s)
1.6
1.8
2
Io1 (A)
10
0
Io2 (A)
-10
0.6
10
0
-10
0.6
Figure 5.10: Output impedance ofUPS#2 and output currents of the
UPS#1 and UPS#2 in soft-start operation (TST =0.1s
and LDo =80H).
obtained based on a hierarchical control energy management.
The system starts to be connected to the grid, with Pg∗ = 1000W and Q∗g = 0V ar.
At t = 4s, the system is disconnected from the grid, and the two UPS units operate in
island mode sharing the overall load. At t = 6s, UPS#2 is disconnected, and UPS#1
supplies all the power to the Microgrid. Notice the proper transient response, as well as
the good power regulation of the system.
5.9 Experimental Results
Two 6-kVA single-phase UPS units were built and tested in order to show the validity of
the proposed approach. Each inverter consisted of a single-phase insulated-gate bipolar
88
Chapter 5 : Hierarchical control for flexible Microgrids
Figure 5.11: Dynamic performance of two inverters using the
hierarchical control strategy.
transistor full bridge with a switching frequency of 20kHz and an LC output filter, with
the following parameters: L=500H, C=100µF, Vin =400V, and Vo =220 Vrms at 50Hz .
The impedance of the lines connected between the inverters and the load was intentionally unbalanced; ZL1 = 0.12 + j0.028, and ZL2 = 0.24 + j0.046. The controls for these
inverters are formed by three loops, namely, an inner current loop, an outer P I controller that ensures voltage regulation, and the power-sharing controller. The first two
loops were implemented by means of a TMS320LF2407A fixed-point 40-MHz digital signal processor (DSP) from Texas Instruments. The power sharing controller was
implemented by using a TMS320C6711 floating-point 200-MHz DSP. The connection
between the two DSPs was made through the host port interface of the 6711. This solution was used only in the design process. Afterward, within the developing process,
we use a single fixed-point DSP TMS320C2811 as a controller. Thus, the cost and
complexity of the control board are further reduced.
The DSP controller also includes a PLL block in order to synchronize the inverter
5.9 : Experimental Results
89
4000
3000
UPS # 2
disconnected
P(W)
2000
P1
P2
Pg
1000
0
Grid connected
-1000
0
1
2
Islanded
3
4
5
6
7
8
9
t(s)
4000
Q(W)
3000
2000
Q1
Q2
Qg
1000
0
-1000
0
1
2
3
4
5
6
7
8
9
t(s)
Figure 5.12: Active and reactive-power transients between
grid-connected and islanded modes (Y-axis: P=1
kW/div, Q=1 kVAr/div).
Figure 5.13: Active power dynamic during transients changes from
grid-connected and islanded modes.
90
Chapter 5 : Hierarchical control for flexible Microgrids
Figure 5.14: Dynamic performance of the output currents when
sharing a pure 40F capacitive load. (a) Connection. (b)
Disconnection (Y -axis: 4 A/div).
Figure 5.15: Output currents of the UPS#1, UPS#2, UPS#3, and
UPS#4 in a) soft-start operation (TST =0.1s and
LDo = 80mH) and b) disconnection scenario.
with the common bus. In this situation, the static bypass switch is turned on, and the
soft-start operation and the droop-based control are initiated. The first set of experiments considers a resistive load. Figure 5.17 shows the output currents of every unit
and the circulating current (io1 − io2 ) for sudden changes from no load to full load and
5.9 : Experimental Results
91
Figure 5.16: Steady state of the output currents when sharing a pure
40µF capacitive load (X-axis:10 ms/div; Y -axis: 5
A/div).
vice versa. These results show an excellent dynamic response for the proposed controller. As it can be seen, the circulating current remains very small, even for no-load
conditions.
Furthermore, the supply of a purely capacitive load of 40F is evaluated. Figure 5.12
and Figure 5.14 show the steady-state and the transient responses of the output currents,
respectively. The sudden connection of the capacitor to the ac bus causes a high current
peak during the instantaneous charge process (see Figure 5.14(a)). The nonsinusoidal
waveforms of these currents appear since the pure capacitive load compromises the
performance of the inner voltage control loop. As it can be seen, the proposed control
achieves a good load-sharing capability in the system. The final experiment consists
in supplying a nonlinear load. Figure 5.18 shows the load voltage and current. The
measured output voltage THD was about 2.1%.
92
Chapter 5 : Hierarchical control for flexible Microgrids
Figure 5.17: Transient response of the output currents and the
circulating current (X-axis: 50 ms/div; Y -axis: 20
A/div).
Figure 5.18: Waveforms of the parallel system sharing a nonlinear
load. Output voltage and load current (X-axis: 5 ms, Y
-axis: 20 A/div).
5.10 : Conclusions
93
5.10 Conclusions
The control structure of this chapter was based on the droop method in order to achieve
autonomous operation of each UPS module and how the droop control strategy can be
easily adaptable to the operation of parallel inverters. Moreover, the proposed control
strategy allows for achieving a tight P and Q regulation performance. A small-signal
model was developed to analyze the system stability and to design the values of the
control parameters. Also, experimental results have been presented in order to validate
the proposed control approach, showing a good steady-state regulation and a proper
transient response when sharing linear and nonlinear loads.
94
Chapter 5 : Hierarchical control for flexible Microgrids
C HAPTER 6
C ONCLUSIONS
Finally in this chapter, the conclusions derived from this dissertation thesis are presented. The main contributions of this thesis are summarized and their publication in
international conference proceedings and international journal articles will be synthesized. In addition, general conclusions and the future lines of research proposed from
the thesis will be discussed.
6.1 Key Contributions
Firstly, in chapter II a review of the state of the art was introduced based on on the
analysis, system stability and power management control starting from a single voltage
source inverter to a number of interconnected DG units forming flexible Microgrids
showing:
⊲ Different control strategies based on droop control characteristic.
⊲ Inner voltage and current loops (proposed as a multiple-loop control scheme).
⊲ Operating modes of a Microgrid applying the concept of primary, secondary and
tertiary control loops conceived as a control hierarchical strategy.
In chapter III, a novel control for VSIs with the capability of flexibly operating gridconnected and islanded mode based on adaptive droop control strategy was proposed.
95
Chapter 6 : Conclusions
96
In addition, active and reactive power can be decoupled from the grid impedance in
order to injected the desired power to the grid. An islanding detection scheme in order
to achieve capability transition under unplanned scenarios was introduced. The main
contributions of this chapter were:
⊲ A dynamic system model based on adaptive droop methodology using Padé approximation.
⊲ A novel control for injecting the desired active and reactive power independently
into the grid for large range of impedance grid values was presented. This control
is based on a parameters estimation provided by an identification algorithm.
⊲ Enhancement of the classic droop control method able to decouple active and
reactive power flows.
⊲ Phase and amplitude synchronization algorithm was presented, ensuring smooth
and safe reconnection between the microgrid and the utility main when the fault
is cleared.
In chapter IV, a droop control method was proposed for voltage dip mitigation and
reduction of the harmonic distortion of the output voltage when linear and non-linear
loads are connected. A detailed analysis has shown that the novel adaptive droop control
strategy has superior behavior in comparison with the existing droop control methods,
ensuring efficient control of frequency and voltage even in presence of voltage sags. At
the same time, the converter provides fast dynamic response and active power to local
loads by injecting reactive power into the grid providing voltage support at fundamental
frequency. Although the developed method is quite simple in theory, parameter tuning
difficulty in practical tests must be considered. Based on the power stage configuration
regarding the dependence of the maximum value of the inductance line impedance, the
maximum active power flow transferred from or to the grid can be controlled.
The control technique was applied to a PV inverter connected through a decoupling
inductance to the main grid. The contributions in this chapter were:
6.1 : Key Contributions
97
⊲ A dynamic model design and a small signal analysis, showing system performance and stability.
⊲ Using the basis of the droop characteristic, a new control strategy was proposed,
providing all the desired active power given by the PV source.
⊲ The validity of the proposed control showed ride-through capability to the system,
even if a voltage sag is presented in the grid.
Finally in chapter V the incorporation of a hierarchical control was proposed, even if
connecting several parallel line interactive UPS units, providing power injection accuracy or avoiding system sensibility to the grid parameters during power line mismatches
of the supply line. Frequency and voltage amplitude regulation based on different levels
of modeling, control and analysis are taken into account, as well. Also, the control of
UPS inverter is important to minimize the harmonic content of the output voltage and
it achieves a good load sharing capability even when supplying as local as non-linear
loads. The disconnection of the UPS does not produce any overcurrent thanks to droop
control strategy for every UPS that accommodate properly the output currents to the
amount of load without critical transients. The main achievements of this work can be
summed up as follows:
⊲ A control scheme for parallel connected UPS systems based on a hierarchical
control strategy avoiding critical communications among UPS units.
⊲ Active and reactive power regulation control and effectiveness of the proposed
method under highly unbalanced power lines, sharing non-linear loads.
6.1.1 Journal Publications
J1. J. M. Guerrero, J. C. Vasquez, J. Matas, J. L. Sosa and L. Garcia de Vicuña.
Control Strategy for Flexible Microgrid Based on Parallel Line-Interactive UPS
Systems, IEEE Transactions on Industrial Electronics, Vol. 56, pages 726-736.
March 2009.
Chapter 6 : Conclusions
98
Table 6.1: Main Contributions
Chapter
2
3
4
5
Contribution
P ublication
Revision of Microgrids and proposal control
[B1]
Voltage Sags mitigation
[J2], [C2], [C3]
Adaptive Droop for line Impedance Variations
[J3], [C1]
Multiple Inverters and Hierarchical Control
[J1], [C4]
I.F actor
N/A
2.216
2.216
2.216
J2. Juan C. Vasquez, Rosa A. Mastromauro, Josep M. Guerrero and Marco Liserre, Voltage Support Provided by a Droop-Controlled Multifunctional Inverter,
(Forthcoming to be included in IEEE Transactions on Industrial Electronics (TIE)).
J3. J. C. Vasquez, J. M. Guerrero, A. Luna, P. Rodriguez, R. Teodorescu, Adaptive
Droop Control Applied to Voltage Source Inverters Operating in Grid-Connected
and Islanded modes, (Forthcoming to be included in IEEE Transactions on Industrial Electronics (T-IE)).
6.1.2 Conference Publications
C1. J. C. Vasquez, J. M. Guerrero, E. Gregorio, P. Rodriguez, R. Teodorescu and F.
Blaabjerg, Adaptive Droop Control Applied to Distributed Generation Inverters
Connected to the Grid, IEEE International Symposium on Industrial Electronics
(ISIE’08). Pages 2420-2425. Jun. 30, 2008
C2. R. A. Mastromauro, M. Liserre, A. dell’Aquila, J. M. Guerrero and J. C. Vasquez,
Droop Control of a Multifunctional PV Inverter. IEEE International Symposium
on Industrial Electronics (ISIE’08), pages 2396-2400. Jun. 30, 2008.
C3. J. Matas, P. Rodriguez, J. M. Guerrero, J. C. Vasquez, Ride-Through Improvement
of Wind-Turbines Via Feedback Linearization, In IEEE International Symposium
on Industrial Electronics (ISIE’08), Pages 2377-2382, Jun. 30, 2008.
C4. J. M. Guerrero, J. C. Vasquez, J. Matas, J. L. Sosa and L. Garcia de Vicuña,
6.2 : General Contributions of the Thesis
99
Parallel Operation of Uninterruptible Power Supply Systems in Microgrids,
12th European Conference on Power Electronics and Applications (EPE’07),
sept.2007.Page(s): 1-9.
6.1.3 Book Chapters
B1. Josep M. Guerrero and Juan. C. Vasquez, Uninterruptible Power Supplies, The
Industrial Electronics Handbook, Second edition, Irwin, J. David (ed.).
6.2 General Contributions of the Thesis
This thesis has presented an analysis, simulation and experimental results focusing on
modeling, control, and analysis of DG units, according to the following steps:
⊲ Control-oriented modeling based on active and reactive power analysis
⊲ Control synthesis based on enhanced droop control technique.
⊲ Small-signal stability study to give guidelines for properly adjusting the control
system parameters according to the desired dynamic response
This methodology has been extended to microgrids by using hierarchical control applied to droop-controlled line interactive UPSs showing that:
⊲ Droop-controlled inverters can be used in islanded microgrids.
⊲ By using multilevel control systems the microgrid can operate in both gridconnected and islanded mode, in a concept called flexible microgrid.
Improvements to the conventional droop method are required for integrate inverterbased energy resources based on:
⊲ Improvement of the transient response
Chapter 6 : Conclusions
100
⊲ Virtual output impedance: harmonic power sharing and hot-swapping
⊲ Adaptive droop control laws
The proposed hierarchical control required for flexible Microgrids consisted of different
control levels, as following:
⊲ Primary control is based on the droop method allowing the connection of different
AC sources without any intercommunication.
⊲ Secondary control avoids the voltage and frequency deviation produced by the
primary control. Only low bandwidth communications are needed to perform
this control level. A synchronization loop can be added in this level to transfer
from islanding to grid connected modes.
⊲ Tertiary control allows the import/export of active and reactive power to the grid.
Additional features were also required in order to manage a flexible Microgrid:
⊲ Voltage ride-through capability, by controlling the injection of reactive power to
solve grid voltage sags.
⊲ Grid impedance estimation, to inject accurately active and reactive power as well
as to detect islanding operation.
⊲ Power-frequency droops used effectively contribute to ensure power sharing.
6.3 Future Work
The aforementioned conclusions in this thesis lead to several proposals for future research work being developed at present, at both a scientific and technical level of development of projects as:
⊲ DC coupling microgrids. This line of research addresses an open field for new renewable energy power-management control strategies. New scenarios emerge for
6.3 : Future Work
101
Distributed Generation systems, electrical power quality, reliability and flexible
operation in Microgrids
⊲ Integrated energy storage systems. These systems operate within varying environments and electrical conditions, and in many different types of battery technologies. Because each technology has advantages under specific operational
conditions, it is important to understand the capabilities and limitations of each
storage technology. In the same way, although electrical energy storage is a wellestablished market, its use in PV systems is generally for stand-alone systems.
The final goal is to develop and integrate energy storage systems specifically designed and optimized for grid-tied PV applications.
⊲ Improving the hierarchical control strategy. Due to political and economic interest and complexity, energy management of Microgrids demand new control
strategies imposed for hard power quality standards, based on intelligent/adaptive
algorithms.
Nowadays, the microgrids are not in an advanced stage of clean energy development. That is why the future of the microgeneration and electricity distribution will
depend on the development of smart grids as DER-based microgrids. Also, the use
the renewable energy sources and advantages of the microgrids such as reliability, efficiency, quality of service, and network support makes these systems very competitive.
102
Chapter 6 : Conclusions
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